Loans myths and reality research work. Loans in our life. The myth of debt restructuring
What person has not dreamed of borrowing money without paying anything for their use? Having understood the essence of lending, many borrowers stopped believing in such a possibility, but there are those who still hope for a miracle. It is for such people that the programs of so-called interest-free loans offered by some banks are designed. It should be noted that financial institutions they know how to present these loans in such a way that not even every knowledgeable person will immediately find a catch.
Where is the "bite"?
Since an interest-free loan is mainly a marketing ploy, to make it more attractive, banks offer it directly at retail outlets, where people's stress resistance is greatly reduced due to the proximity of the goods. It is in such conditions that citizens are more prone to spontaneous, and sometimes completely illogical decisions.I must say that now almost all serious financial institutions have excluded interest-free loans from their lists of loan offers. Such technology continues to be used only by small banks that do not occupy a serious position in the market. For them, this is a way to quickly get new borrowers for themselves by luring them away from competitors pseudo favorable conditions.
Interest-free loan - where is the bank's benefit "hidden"?
Often in offers for interest-free loans you will not even find the word “bank”, but, of course, in most cases it is these financial institutions that are behind such advertising. At the same time, in a loan agreement for such a “free” loan, very often there are places printed in small print. It is in them that one should look for the truth about a loan without interest.It is not uncommon for a 0 to appear in the interest rate column, and positive interest values appear elsewhere in the loan agreement. Only there they are called differently -. The bank may have several options for its collection. So, it can be paid by the borrower immediately when applying for a loan (sometimes in this form it can still be called insurance), or later - along with each monthly payment. Some banks may even charge a fee for reviewing an applicant's application.
Sometimes banks may apply a combined earnings scheme. With it, they charge a certain commission immediately upon issuing a loan. The very same loan for a short time (no more than six months), the debtor will actually pay without interest. In fact, these percentages were already paid to them at the beginning. Remember commission? If the borrower does not repay the debt during this time, in the future he will begin to repay it already with interest, but at the same time their value will be very large (sometimes up to 70% per annum).
Sometimes, in order to obtain benefits, within the framework of interest-free lending, banks cooperate with insurance agencies. At the same time, the borrower is obliged to buy a policy from the same company. The bank's profit will be included in the cost of the policy, which under normal conditions can cost several times cheaper. After signing the insurance contract, the agency will begin to deduct a commission to the bank from each insurance paid by the borrower.
Not only banks
More than one bank came up with the idea of interest-free lending. The same technology began to be used by themselves outlets, promising its customers installments for certain products. However, not everything is fair here. As a rule, the technology of earning a store on these "promotions" is quite simple.A few weeks before it starts, the store raises the prices of goods that are supposed to be sold in installments. Such actions of the seller, as a rule, remain "behind the scenes" for consumers - those are supposed to see only the action itself. Subsequently, the buyer's debt can be assigned by the store to the bank. At the same time, a “discount” is made to the credit institution just for those 15-20%, by which the goods have risen in price earlier.
Nikulitsa Elena. Gridasova Anastasia
I. Introduction 3
1. Relevance of the topic 3
2. Goals and objectives of the study 4
II. Theoretical part 5
3. History of credit and its significance for a person 5
4. Classification of loans 6
III. Practical part 9
5. Analysis of household loans 9
6. Comparative analysis of two popular loans among the population. thirteen
IV. Conclusion 17
7. Conclusion 17
List of used literature and sources 18
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Federal Agency for State Reserves
Federal State Budgetary Educational Institution
Torzhok Polytechnic College
Scientific - research: "Credits in the life of a modern person"
Completed by: Nikulitsa E.S.
Gridasova A.S.
Teacher: N. V. Merkurieva.
Torzhok, 2017
Sheet
I. Introduction 3
1. Relevance of the topic 3
2. Goals and objectives of the study 4
II. Theoretical part 5
3. History of credit and its significance for a person 5
4. Classification of loans 6
III. Practical part 9
5. Analysis of household loans 9
6. Comparative analysis of two popular loans among the population. thirteen
IV. Conclusion 17
7. Conclusion 17
List of used literature and sources 18
I Introduction
- Relevance.
In the recent 80-90s, few people from the population knew what a loan was and very few used it. financial instrument. Loans were mainly used by organizations, collective farms and state farms. There was a single monopoly in the banking system - Sberbank.
Were consumer loans for the population for a short period, for example, it was possible to get a sofa for a period of 6 months on credit. Such loans enjoyed little popularity among the population. People did not need loans, they had enough wages to live on.
In today's society, even children know what credit means. Starting from the younger generation and ending with pensioners, all people are "entangled" in loans and this does not surprise anyone. On the contrary, it is difficult to find a person who does not have debts. This is facilitated by a large and extensive network of various banks, financial institutions and pawnshops. Easy and "step-by-step" availability of loans.
A large assortment banking services from year to year expands and offers the most attractive options for the consumer. Promotions are held and prizes are drawn in order to attract customers.
Due to the fact that purchasing power The population is low, and the needs are growing every day, a person can easily apply for a loan. This decision is not always fully conscious and thought out. Here is an example from life. Another New Year, in order to cheerfully meet him, there was not enough music center. And then the action in the hypermarket, you can get the same center on credit. It's said and done. The holidays are over, and there was a desire to repay the loan ahead of schedule, it turned out to be possible, but with a decent overpayment. But by and large, the need for this loan was very small, and the costs were tangible.
Any person, regardless of whether he officially works or not, can find a loan option that suits him. It is easier for a person who is officially employed to apply for a loan and choose a more profitable option. Lack of work is not an obstacle to obtaining a loan. For this, there are various types of express loans.
Some banks send credit cards by mail to attract borrowers. In this case, you do not even need to go to the bank, it is enough to activate the card at an ATM.
From this it follows that the topic of lending in the life of a modern person is relevant not only today, but also in the future.
2. Goals and objectives
Target:
- Consider the role of credit in the life of a modern person.
Tasks:
- to study the theoretical aspects of the presented topic;
- collect and analyze information on public loans;
- make a comparative analysis of two popular loans among the population;
II. Theoretical part
3. Loan history
People have been using loans since the time of King Solomon. True, then, for the untimely repayment of the debt, they could send the debtor into slavery to the creditor. And later, Solomon ordered that the borrower be responsible to the lender not with his freedom and life, but with his property. When a person took a loan and did not repay it on time, a special pole was driven in front of his house, on which the name of the lender was indicated, to which all the property of the borrower passed. This pillar was called a mortgage, which literally means "pledge".
At first, lenders did not earn anything on loans. It was not a business, but rather a forced measure for those peasants who did not have a sufficient harvest. Such an unfortunate peasant went to a more prosperous neighbor to borrow grain so as not to die of hunger. Having received 1 sack of wheat, the "borrower" had to return one and a half or even two sacks.
True, there was no guarantee that in a year the peasant would be more lucky, and he would be able to repay the debt to his neighbor. If a year later the debt was not returned, the unfortunate borrower passed into debt slavery to his creditor.
The Church was a fierce opponent of such behavior on the part of creditors and advocated not demanding interest from borrowers and even forgiving their debts. So, in the Gospel it is written: “... give us a loan, not expecting anything ...”
Yes, such propaganda is now clearly lacking for some bank customers.
After a while, in the 17th century in England, they began to provide loans at predetermined interest rates. In Russia, interest on loans began to be charged only in the middle of the next century, and then at a rate not higher than 6% per annum.
Historically, the forerunner of modern credit is usurious credit. The division of the primitive community in the period of its decomposition into poor and rich families, the accumulation of wealth in some hands and the need for money in others created the conditions for usurious credit. Usury capital in the ancient world was provided mainly to small commodity producers (peasants) and slave owners. Merchants and tax-farmers acted as usurers-creditors in the slave-owning society. Temples played a significant role, for example, in Greece, the Delphic Temple. Under the feudal system, usurious credit also appeared in two main forms: loans to small commodity producers (peasants and artisans) and feudal lords.
As under slaveholding, so under feudalism, and under feudalism, small producers needed money to buy means of subsistence and pay taxes.
The need of slave owners and feudal lords (kings, nobles) for money is due to their spending huge amounts of money on buying luxury goods, building magnificent houses, waging wars, etc.
Banks arose as states formed. Initially, private banks were created, for example, the “family bank” was in medieval Veliky Novgorod, where usury flourished. With the advent of religion, the states began to revive the temple, monastic, state and provincial "banks". Their main activity is to raise funds for the construction of buildings and structures, temples, and the maintenance of armies.
Approximately 4 - 5 thousand years ago, taxes (in the form of tributes, gifts) and loans, financial control and "ancient audit" (in the form of advice from knowledgeable people for those who are not very knowledgeable) are known. Even prescribed forms of a kind of insurance.
Currently, loans are a financial instrument necessary for the development of the economy.
4. Classification of loans
Loan classification | Types of loans | Definition |
1. Types of loans by security |
| They are loans without collateral - unsecured loans without guarantors and guarantors |
| For example, if the pledge covers only part of the funds needed for repayment, or the guarantor (guarantor) vouches for the payment of only part of the debt |
|
| Pledge that excludes the loss of funds by the creditor, bank guarantees or a guarantee of one or several people - make lending conditions more accessible |
|
2. By payment |
| Receiving finance in debt, the debtor pays every period (monthly, quarterly, annually ...) part of the debt, as well as interest on the use of funds. This type of loan is the most popular and most widespread. |
| These are loans without a fixed interest rate. Depending on fluctuations in the market, the rate may “float”, i.e. look like a wave. Mostly applicable to long-term loans |
|
| The loan is issued at a certain percentage from the issuance to the last payment |
|
| It contains a fixed interest rate (basis), and a variable part |
|
Often there is a similar target loan for a specific purchase, called installment. Its principle is slightly changed - an appropriate agreement is concluded between the bank and the seller, and the seller pays interest (sometimes very low). Almost always, the seller compensates for these percentages with an inflated price. In some cases, a large seller himself becomes a creditor, and, selling goods in installments, is ready to wait a little to receive money. |
||
| The principle is simple - upon receipt, partial or full repayment of a loan, the debtor is obliged to pay an appropriate fixed fee for use. Such transactions are quite rare. |
|
3. By purpose |
| Funds received in debt can only be used for a specific purpose specified in the loan agreement |
1. For housing | ||
2.Car loan | ||
3.Land | ||
4.Consumer | ||
5.Educational | ||
6. Brokerage | For the circulation of securities, a loan is issued to a stock broker, the security is purchased securities |
|
7.Others. | Purposes not listed but agreed upon and approved by the lender |
|
| The debtor can spend the money received at his own discretion. |
|
4.Depending on the financial and social status of the borrower | This category should not be confused with the poor, or extremely poor - this category of people often consists of those who are unable to prove income, or who have no desire. Income in this category may consist of dividends, interest, profits from the rental of housing, business, and therefore the approach to lending to each is special. |
|
| It is difficult to control the cash flow, as well as the income of this category of people, therefore, for individual entrepreneurs, sometimes more stringent, unique lending conditions |
|
| Often, the profitability of organizations is strictly declared, the lender can draw up a schedule and observe the development trend of the enterprise. Since incomes are high, and the word “enterprise” itself sounds like “reliability”, such loans are issued with a low interest rate, a large maximum amount |
|
| Pension credit is issued to the elderly, as well as to persons receiving a pension. The amount of this loan is very dependent on the amount of social payments, as well as the age of the borrower. Such transactions do not differ in favorable conditions, duration and amounts. |
|
Students receive loans for food, housing, etc. |
||
Issued to people to participate in a tender, competition or auction. Constituting an insignificant part of the prize, they imply a special approach to each borrower |
||
5. Depending on the lender |
| A rare type of loan that involves very high interest and material collateral. Now it is quite rare, in countries with an underdeveloped credit system |
A loan between family members, properly executed |
||
| The most popular loan now, when a bank or a similar credit organization acts on the part of the lender, and on the second - an individual or legal entity |
|
| After the transaction is completed, the debtor receives funds |
|
| Issued a plastic card(often instant, within 15 minutes), and the amount is transferred to it |
|
| The issued plastic card has a zero balance, however, the cardholder is given the opportunity to "go into the red" for a certain amount (its maximum is called the credit limit), and the interest rate is charged depending on the use of credit funds |
|
| Similar to the previous one, however, it has the possibility of an overdraft - a short-term exit from the balance and credit limit. A revolving overdraft is also called a revolving loan. |
|
| Creditor and debtor are two or more different banks |
|
| Deal among legal entities, or between a company and an individual |
|
| A loan issued by a state bank under certain conditions is more favorable. Often, loans issued by banks and subsidized by the state are also called state loans, for example, preferential car loans, youth loans, etc. |
|
Investments from one or more states to another |
||
6. By urgency |
| Line of credit often used by brokers |
| Interbank loan for one night |
|
Up to three months |
||
Up to a year |
||
From one year to five |
||
| Over five years |
|
7. Small loans available to the public | A prerequisite for lending is the availability of easily realizable collateral, the amount and interest rate directly depend on the security |
|
Issued almost instantly (often online), characterized by a high interest rate, a low maximum amount and no collateral. The main condition for receiving is the absence of large debts from the recipient |
||
| Issued at points of sale of equipment, as well as supermarkets |
III. Practical part
- Analysis of household loans
Wages are increasing at a slower rate. The needs of the population are growing. The credit policy of banks is guided by the needs of the population. Loan rates are floating. All this speaks of the growth in lending.
Let's analyze some data on the bank loans market.
*data in billion rubles
As you can see from the figure, the total volume of loans as of March 1, 2017 increased by 33% compared to January last year. The volume of loans issued to the population also increased, but by 36.29% compared to the level of January 2016.
*data in billion rubles
But the share of loans individuals in total loans increased over this period by only 0.6%
What type of loans for individuals do Russians prefer most? Have there been any changes in the "credit preferences" of citizens?
Let us conditionally divide loans from individuals into loans for construction (and the purchase of real estate) and consumer loans.
The share of loans for construction in the total volume of loans for individuals has significantly decreased over this time - minus 2.47% compared to March last year or minus 1.75% compared to the data as of 01/01/2016.
And since the total amount of loans issued to individuals is growing, it is reasonable to conclude that there is an increase in the volume of consumer lending, or rather “loans for small things in life”.
- Comparative analysis of two popular loans among the population
To date, the most popular loans are mortgage and consumer.
Mortgage | consumer credit |
Definition |
|
a long-term loan provided to a legal entity or individual by banks secured by real estate: land, industrial and residential buildings, premises, structures. The most common use of a mortgage in Russia is the purchase by an individual of an apartment on credit. In this case, as a rule, newly bought housing is mortgaged, although it is possible to mortgage an apartment already owned. Note that a mortgage is a public pledge. When real estate is mortgaged, the bodies registering transactions make appropriate records that the property is encumbered with a pledge. Any interested person may require an extract from the State Register of rights to real estate and transactions with it. | credit provided directly to citizens (households) for the purchase of consumer goods. Such a loan is taken not only for the purchase of durable goods (apartments, furniture, cars, etc.), but also for other purchases ( mobile phones, household appliances, food). It acts either in the form of the sale of goods with a deferred payment, or in the form of a bank loan for consumer purposes, including through credit cards. In this case, a fairly high percentage is charged. |
Loan types |
|
By property:
According to the purpose of lending:
By type of lender:
By type of borrower:
According to the method of refinancing. |
|
pros |
|
|
|
Minuses |
|
|
|
Required documents for obtaining a loan |
|
|
Some banks now issue so-called express loans, where a certificate of income is not required, the client himself indicates the amount he receives. |
Loan terms |
|
Fluctuation of terms of the credit within 1 - 30 years. | The standard practice for consumer finance remains either short-term loans or loans for a period of 3-5 years. |
Rates |
|
Average mortgage rates in various companies range from 11 to 16%. | Average consumer loan rates in various companies vary from 12 to 27%. |
IV. Conclusion
7. Conclusion
Loans in the life of a modern person play a significant role, since the income of the population cannot always meet its needs.
Summing up our work, we can say thatcredit policy of banks is guided by the needs of the population. Loan rates are floating. All this speaks of the growth in lending.
The total volume of loans as of March 1, 2017 compared to January last year increased by 33%. The volume of loans issued to the population also increased, but by 36.29% compared to the level of January 2016. This suggests that the population is increasingly resorting to lending services, because thanks to them you can meet your needs.
The share of loans for construction in the total volume of loans for individuals has significantly decreased over this time - minus 2.47% compared to March last year or minus 1.75% compared to the data as of 01/01/2016. It means that mortgage is no longer in demand because of the high stakes on it, but still remains popular.
And since the total amount of loans issued to individuals is growing, it is reasonable to conclude that there is an increase in the volume of consumer lending, or rather “loans for small things in life”. After all, it is this type of loan that the population actively uses for large purchases, such as the purchase of household appliances, telephones, computers and others. A person's income cannot allow him to make such a purchase, but with a loan this is easy to do.
List of used literature and sources
1. https://torzhok.bankiros.ru/credits
2. http://www.banki.ru/products/credits/
3. http://www.sberbank.ru/ru/person/credits/money
4. http://pravopark.ru/grazhdanskoe/kredity-i-zajmy/potrebitelskij-kredit/
5. http://studopedia.ru/7_45351_ipotechniy-kredit.html
6. http://www.sberbank.ru/ru/person/credits/home
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Subject: Mortgage and how to repay it.
student 9 "B" class
MAOU "Secondary School No. 3"
Head: Tetueva Gulbahar Eskanderovna,
mathematic teacher
MAOU "Secondary School No. 3"
Introduction ………………………………………………………………………. 2
I. What is a mortgage ………………………………………………………………..3-5
II. Advantages and disadvantages of a mortgage………………………………………. 6-7
III. Loan payment options……………………………………………….8-11
IV. Early repayment of a mortgage…………………….. ……………………...11-16
V. Advice to the borrower ……………………………………………………………….16-17
VI. Conclusion………………………………………………………………………17-18
VII. References…………………………………………..………….. 19
Introduction
It is vital for every family to have their own apartment or house - where they raise children, where they spend evenings in the family circle, playing with a dog or just lying on their favorite sofa with a book in their hands. But, even with a job, not everyone can buy a home. And at the current rate of growth in real estate prices, not everyone can afford to save (unless, of course, the family income does not exceed the average salary by several times). The cost of even the most modest apartment in the regional cities of Russia is incomparable with income .... But how I would like to live in warm climes! Or at least somewhere in the middle lane. How to buy an apartment? It is clear that one must either save or borrow. And this amount can only be borrowed from a bank. Since in my previous research work I studied some concepts related to loans, banks and inflation, the concept of "indebtedness" is not new to me. But why buying an apartment is called a mortgage and what nuances are associated with paying off a debt in a mortgage are not entirely clear to me. Before me was a task requiring research, to which I decided to devote my work.
Objective- Consider the concept of mortgage lending and how to repay it.
1. Conduct a survey of different age categories of people on the subject of awareness of the possibilities to buy an apartment.
2. Study the literature on the topic.
3. Consider the concept of a mortgage.
4. Consider different loan repayment options. Solve problems for calculating payments under the terms of mortgage lending (taking approximate values).
5. Make a conclusion.
Methods: analysis, proof, comparison.
Relevance of the topic: A mortgage loan is an opportunity to purchase housing in a short time. It is this state loan that is the only way for young families to purchase housing!
Hypothesis: If a mortgage loan is practically the only way to buy an apartment on credit, is it profitable?
Object of study: Loan payment options and the possibility of early mortgage repayment.
Subject of research: calculation of various mortgage payment options.
I. What is a mortgage
Mortgage (from the Greek hypotheke - pledge) is a type of pledge in which the pledged property (they are real estate objects, as a rule, this is land and buildings on it) remains in the possession of the mortgagor until the maturity date. For the use of the issued loan, you pay the bank the interest specified in the loan agreement and return the borrowed funds in the form of monthly payments to the bank, also established by the loan agreement.
The term mortgage in Russia is usually used in connection with the solution of housing problems. The most common use of a mortgage in Russia is to buy an apartment on credit. In this case, as a rule, newly bought housing is mortgaged, although it is possible to mortgage an apartment already owned. Mortgage loans are issued by banks, and lending conditions are different for everyone. Mortgage has existed in Russia for quite a long time, but is still not in wide demand. The reason for this situation becomes clear if you look at the world rankings of this sector. So, last year, specialists from the PennyLaneRealty office real estate department systematized data on housing costs and mortgage rates from around the world and published their findings. A Russian is offered a mortgage at 10-15% per annum for 20 years. This means that the borrower must pay monthly an amount equal to 2-3 average salaries, and in general, the cost of housing will exceed the original value by 2-2.5 times.
Not surprisingly, a country with such indicators takes an "honorable" 47th place in the list, just behind Honduras. In comparison, a mortgage in Denmark, which tops the list, is much cheaper for its citizens: the borrower pays only 11% on top of the cost of living space for the entire time. We have 200-250%, they have 111%. Lending rates in the countries leading the list (Europe, USA) range from 1.3 to 4.6% per annum. This situation has been going on for quite a long time and efforts are periodically made to change it.
In 1997, by decision of the government of the Russian Federation, the Agency for Housing Mortgage Lending was established. 100% of the shares belong to the state represented by federal agency for federal property management. The Agency's activities are aimed at creating equal opportunities for obtaining mortgage loans by all citizens of Russia, regardless of social status, education, family composition, place of residence or registration.
What is the difference between a mortgage under the state program.
At a time when mortgage rates in banks are constantly rising, mortgage rates are State program remain at the same level or decrease altogether, as happened in the last period.
Lending under the Federal Mortgage Standard (FIS). The main advantage of FIS lending is low interest pegged to the CBRF refinancing rate. Moreover, the growth of the refinancing rate does not affect the conditions for already issued loans. The status of an organization authorized to work in accordance with the Federal Mortgage Standards automatically means state control over its activities in terms of the quality of service for the Borrower.
Benefits of a mortgage under the State Program:
· minimum size down payment - from 20%;
· low interest rates - from 8.3% per annum in rubles;
The maximum loan term is 30 years;
· Age of the Borrowers - up to 65 years;
no moratorium and penalties for early repayment;
· reliable protection of the interests of the Borrower by the State.
For residents of Yugra, a target program "Improvement living conditions population of Khanty-Mansi Autonomous Okrug - Yugra for 2011-2013 and for the period up to 2015", according to which a mortgage can be obtained on preferential terms. (Appendix No. 1)
Popular mortgage programs* today
|
Program / bank |
Property type |
An initial fee |
|
|
Apartment under construction |
|||
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New building - JSC "Khanty-Mansiysk Bank" |
apartment under construction |
||
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New building - JSC "Khanty-Mansiysk Bank" |
apartment under construction |
||
|
New building - JSC "Khanty-Mansiysk Bank" |
apartment under construction |
||
|
finished apartment |
|||
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Mortgage with state support - Bank VTB 24 CJSC |
finished apartment |
||
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Mortgage for the purchase of residential real estate (apartments) - Surgutneftegazbank CJSC |
finished apartment |
||
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Mortgage for equity participation in the construction of residential real estate (apartments) - Surgutneftegazbank CJSC |
apartment under construction |
||
|
Mortgage for the purchase of residential real estate (apartments) - Surgutneftegazbank CJSC |
finished apartment |
II. Advantages and disadvantages of a mortgage.
Main advantage mortgage is that, instead of accumulating the necessary amount for the purchase of housing for many years, it becomes possible to live in new apartment(or home). At the same time, housing purchased on a mortgage is immediately the property of the borrower of the mortgage loan. In new housing, you can register the borrower and his family members. The safety of the operation is ensured by insurance of the risks of loss of ownership of the apartment and its damage, as well as the loss of the borrower's ability to work. In addition, the mortgage has a number of "pluses": the borrower of a mortgage loan is provided with property tax deduction, which actually reduces the mortgage interest rate due to the fact that the borrower will not pay income tax on the amount spent on the purchase of housing and on mortgage interest; a long loan term makes mortgage payments not too large and therefore not too onerous. For certain categories of people, the existence of a social mortgage in their region may be a pleasant surprise.
The most significant disadvantage mortgage is the so-called "overpayment" for an apartment, which can reach 100% or more. Mortgage "overpayment" includes mortgage interest and annual amounts compulsory insurance. In addition, in the process of obtaining a mortgage loan, the borrower has to bear some additional costs, such as payment for services appraisal company and a notary, a bank fee for considering an application for a loan, a fee for maintaining a loan account, etc. Overhead costs in the aggregate can reach 10% of the down payment on the purchase of housing. Another “minus” of a mortgage is a large number of requirements of mortgage banks for borrowers: documentary evidence of income, registration and Russian citizenship, a certain length of service in one place, the ability to present loan guarantors, etc.
The sequence of actions for those who decide to use mortgage lending in the city of Kogalym (information taken from the Kogalym Mortgage Lending Agency).
|
Consultation |
The amount and term of a possible loan · Loan interest ・Amount of down payment List of documents required for obtaining a loan What are the additional processing costs |
|
|
Finding an apartment |
By yourself or with the help of real estate agencies, you find the desired option for yourself. Check the authenticity of the documents for the property for compliance with civil law. In the case of self-selection of housing, the lender's lawyers are involved in the verification. |
|
|
Apartment appraisal |
After choosing housing and checking documents, it is necessary to conduct an independent assessment of the cost of the selected housing. The assessment must be carried out by an accredited organization. |
|
|
Purchase - sale |
The next step is the conclusion of a real estate purchase and sale agreement with the entry into force of the mortgage law (mortgage agreement), a loan agreement and a mortgage. |
|
|
Deal registration |
After signing the above documents, they are handed over to the Main Directorate of the Federal Registration Service for the Murmansk Region for registration. |
|
|
Insurance |
After registration of the transaction, a combined mortgage insurance contract is concluded and provided in credit organization. Insurance costs are borne by the borrower - the buyer of real estate. Usually they are 1% of the loan amount. |
III. Loan payment options
Suppose the loan is approved, the apartment is bought. We need to start paying off our debts. Usually, Russian banks apply two options for payments on the loan - annuity or differentiated payments.
The formula for calculating the monthly annuity payment:
where x is the monthly payment, S is the initial loan amount, P is 1/12 of the interest rate in hundredths, N is the number of months.
The formula for determining which part of the payment went to repay the loan and which part to pay interest is quite complex and without special mathematical knowledge it will be difficult for a simple layman to use it. Therefore, we will calculate these quantities in a simple way that gives the same result. To calculate the percentage component of an annuity payment, you need to multiply the loan balance for the specified period by the annual interest rate and divide all this by 12 (the number of months in a year).,
Where PN- accrued interest, Sn - balance of debt for the period, P- the annual interest rate on the loan. To determine the part that goes to repay the debt, it is necessary to deduct the accrued interest from the monthly payment.
Since the part going to repay the principal debt depends on previous payments, therefore, the calculation of the schedule, according to this method, is calculated sequentially, starting from the first payment.
The annuity formula is quite complicated, so to determine the amount of the annuity, and differentiated payments, it is better to use a mortgage calculator.
|
Loan details |
Payment type |
||
|---|---|---|---|
|
Loan amount (rub.): |
Differentiated payments: |
||
|
Interest rate (%): |
Payments in equal installments: |
||
|
Date of receipt of the loan: |
Amount of payment: |
||
|
Loan maturity (months): |
Dif. payments in equal parts: |
||
|
Monthly commission (%): |
|||
Calculation of differentiated payment
The amount of the main payment is calculated as follows: it is necessary to divide the loan amount by the number of months for which the loan is planned to be repaid, the resulting number will be the main payment. b= S/N, where
b- main payment, S- loan amount, N- number of months.
To calculate the accrued interest, you need to multiply the loan balance for the specified period by the annual interest rate and divide all this by 12 (the number of months in a year). p= Sn* P/ 12,
where p is the accrued interest, Sn is the balance of the debt for the period, P is the annual interest rate on the loan.
To calculate the balance of the debt for the period, i.e. find the value from the above formula, you need to multiply the amount of the main payment by the number of past periods and subtract all this from the total amount of the payment.
Sn= S- (b* n) , where n is the number of past periods.
In the case of an annuity, the client pays the bank the same amount every month, which includes repayment of the principal and interest. Most banks prefer annuity payments because they allow you to earn more on interest (the reason is that the body of debt decreases more slowly than with differentiated payments). However, this payment option also has its advantages. Firstly, the financial burden at the initial stage of loan payments in the case of an annuity is less. Secondly, with the same level of income, annuity payments allow you to take a larger loan amount compared to differentiated payments (this is a consequence of a lower financial burden at the initial stage of payments).
With a differentiated payment, the principal debt is paid in equal installments, and interest is charged on the balance of the loan debt. The monthly payment gradually decreases as payments are made, because interest is accrued on an ever-shrinking body of debt. A differentiated payment is more beneficial in terms of minimizing interest payments. However, there are also disadvantages, which, in fact, are the reverse side of the advantages of an annuity: with differentiated payments, the maximum possible loan amount is slightly less than with annuity, and at the beginning of lending, an increased debt load arises.
For clarity, we will give a specific example of differentiated and annuity payments for lending in the amount of 100 thousand rubles at 11% per annum for a period of 6 months (see tables). As can be seen from the example, in the case of a differentiated payment (without early repayment), the client will pay 24.4 rubles less than with an annuity. For longer terms and amounts, the difference will be more significant (this is especially true for mortgage loans).
Loan payment schedule: Annuity payments
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
Loan repayment schedule: Differentiated payments
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
IV. Mortgage early repayment.
Today, many Russians take loans from banks, while many, weighed down by the debt burden, are trying to pay off the loan ahead of schedule. What is the situation with early loan repayment in our country? What are the limits and fees? How to make early repayment of the loan?
According to AHML, the majority of Russians still try to pay off their mortgage early. In 2011-2012, 14.7% of all accumulated mortgage debt was repaid ahead of schedule. If the average term for issuing a housing loan is 15-17 years, then borrowers, as a rule, deal with payments in 6-7 years, that is, twice as fast. Both savings and maternity capital funds, tax deductions, etc. go to the repayment account.
Previously, fees and penalties were barriers to early repayment. To cool down too hasty borrowers, the bank directly or indirectly prescribed sanctions for early repayment in the loan agreement. It could be either a fixed amount or a portion of the interest that the bank would have received on just-in-time repayment. Such measures caused a storm of protest among conscientious borrowers - as a result, the authorities met them halfway and revised the provisions of the law on early repayment of loans. So, from November 1, 2011, amendments to the Civil Code of the Russian Federation came into force, according to which it is possible to repay the loan ahead of schedule without any penalties and at any time. The only requirement for the borrower is to notify the lender of his intentions, and this must be done no later than 30 days before the date of the planned early repayment. The notification is submitted to the creditor bank in writing and is considered by the bank within 3-5 working days. After that, appropriate changes are made to the borrower's payment schedule, on the basis of which the loan can be repaid ahead of schedule (both partially and in full).
For early repayment of a loan, a bank usually offers two options: reducing the loan term and reducing monthly payments. In fact, in addition to the two mentioned methods of early repayment of the loan, there are others. Let's consider them in more detail.
1 option. The loan term is shortened, and the size monthly payment loan does not change. Obviously, this option is used, as a rule, for annuity payments: the point is precisely to keep the size of the monthly payment unchanged. Many people think that it is very convenient when the payment is the same every month and there is no need to constantly specify how much to pay off the loan. In the case of differentiated payments, the amount of the monthly payment is constantly decreasing.
Plus- interest payments on the loan are reduced.
Minus- Monthly debt load is not reduced.
Option 2. The loan term does not change, and the size of the monthly payment on the loan decreases. This option is used for both annuity and differentiated payments.
Plus- Monthly debt load is reduced.
Minus- interest payments on the loan are reduced insignificantly.
3 Option. The loan term does not change, and the payment of the principal debt is suspended. Attention! Interest payments continue. This option is used only for differentiated payments, since otherwise the meaning of the annuity (the same monthly payments) is lost - several "empty" months appear.
Plus- interest payments on the loan are reduced.
Minus- the debt burden is reduced only for the period of suspension of the payment of the principal debt.
What is better?
For clarity, we present the changed payment schedules for all three options for early repayment, assuming that the borrower paid 40,000 rubles ahead of schedule in the second month of lending (see tables). As can be seen from the calculations, from the point of view of minimizing the overpayment on the loan, the most profitable is the first option of early repayment, namely, reducing the loan term. The reason is that the body of the debt now occupies a more significant share in the monthly payment, it decreases faster and thus the interest payments are rapidly reduced. But from the point of view of reducing the debt burden, the second option is more profitable (reducing the amount of the monthly payment). The third option - suspension of principal payments turns out to be the most unprofitable and is recommended only if you want to reduce your debt burden for a specific short period (in our example, two months).
1st early repayment option: Annuity payment.
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
|
100 000.00 (including 40 000) |
2028.6 (including 40,000) |
2nd early repayment option: Annuity payment
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
|
(including 40,000) |
(including 40,000) |
2nd early repayment option: Differentiated payment.
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
|
(including 40,000) |
(including 40,000) |
Early repayment option 3: Differentiated payment
|
Repayment period |
Monthly payment |
Repayment of principal |
Interest charges |
|
(including 40,000) |
(including 40,000) |
With the full repayment of the loan, a person also saves on interest - the more, the earlier he repays his loan. If the final settlement on it occurs long before the expiration of the loan agreement, the borrower wins seriously on interest, but the bank, on the contrary, loses. It is not surprising that banks are not very fond of borrowers who repay their loans “in advance”: such citizens deprive the bank of profit. As a result, lenders often create obstacles for clients to carry out this procedure. Partial repayment is prohibited much more often: in an agreement with the borrower, the bank requires either to make regular payments according to the schedule, “penny for a penny”, or to pay the entire balance of the debt with interest accrued on the date of early repayment of the loan.
And now let's look at how things are with the early repayment of credit money in Sberbank, VTB 24 and Home Credit Bank.
Sberbank
The largest bank in Russia gives its borrowers the opportunity to repay the loan in a way convenient for them. To calculate payments (including early repayment), you can use loan calculator offered on the bank's website.
Early repayment of a loan at Sberbank occurs according to the following scheme:
1. The borrower replenishes the account from which money is transferred to repay the loan;
2. On the day of the next loan payment (according to the payment schedule), the borrower comes to the Sberbank branch where he executed this loan agreement and notifies the bank of his intention to pay off the loan ahead of schedule. Please note: no one has canceled the clause on notifying the creditor 30 days before the date of early repayment in Sberbank!
3. An employee of the bank draws up an updated loan payment schedule (indicating the recalculated monthly payment), which is countersigned by the borrower;
4. In case of full early repayment, after the transfer of the refundable amount to Sberbank (be sure to ask the bank for a certificate of no debt on your loan!) Your credit account is closed, and the loan agreement is terminated.
Note that Sberbank does not have a moratorium on early repayment of loans, as well as restrictions on the amount of partial early repayment.
VTB 24
The early repayment scheme in this bank is almost the same as in Sberbank. The only fundamental difference is a 3-month moratorium on early repayment on car loans, as well as a fixed minimum amount of early repayment on mortgage loans - this is 15,000 rubles.
Home Credit
This bank has neither a moratorium on early repayment nor a fixed minimum amount of such repayment. Not surprisingly, Home Credit interest rates are high enough to offset the risk of not making a profit if the loan is repaid too quickly.
The burden of interest on the loan speaks in favor of early settlement of mortgage obligations. A simple calculation makes it possible to understand that for the entire term of the loan, the payment of interest results in a double or even triple overpayment over the amount taken. sum of money. So, the sooner you pay off, the more money you can save. Everything is logical, but do not forget about inflation, which, according to real estimates, is about 10-15% per year. In the context of the long-term period, the borrower's income grows due to the growth of wages. This does not mean the growth of income compared to the current prices of the consumer basket, but the growth of income relative to inflation. Here a situation arises when a mortgage loan, having a fixed rate and a constant periodic payment, is repaid monthly based on increased income, and, therefore, gradually becomes a smaller item of expenses for the family budget.
The next argument "against" are the features of the real estate market. When analyzing the dynamics of prices for apartments over a period of up to 10 years, the benefits of investing in real estate become obvious, due to the constant increase in the cost of the latter. In other words, it is likely that the greatest benefit will come not from paying off an existing loan, but using free money to buy a new property or invest in shares. The third feature is that the state returns 13% of all interest paid on the loan. This means that while the borrower pays the loan, he can count on the reimbursement of part of his expenses, which will somewhat reduce the loan burden.
You should be fair and indicate the situations when, nevertheless, it is recommended to repay the loan ahead of schedule. Firstly, it is the availability of free money, which, due to unwillingness or impossibility, is difficult to find a worthy application. Then, of course, the best option is early settlement of the loan. Perhaps the mortgage obligations put too much pressure on the borrower psychologically, there are thoughts that the bank will sooner or later take the housing, and the only way out is seen in early settlement. And, finally, early settlement with the bank should be carried out if the monthly payment eats up more than 40% of the salary, in this case it is simply necessary to use any free money for settlement with the bank.
v.Tips for the borrower
1. When applying for a loan, ask the loan officer if you have the right to choose the method of repayment on the loan (annuity or differentiated payments).
2. When concluding a loan agreement, pay attention to:
· the right of early repayment (term, minimum amount, the presence or absence of penalties); · the availability of options for early repayment of the loan.
3. When choosing an early repayment method, decide for yourself what is more important: reducing the amount of the overpayment or reducing the debt burden.
4. When concluding a loan agreement, ask to write an application for the so-called non-acceptance early repayment of the loan upon receipt of funds to your account opened with the creditor bank.
This is necessary so that you do not have to come to the bank every time and write a special application (as a rule, in order to make an early repayment, you must provide the bank with a written application indicating the amount). Therefore, direct debiting can be very useful if you do not want to waste time traveling to the bank, but intend to transfer money to repay a loan by bank transfer or using ATMs and other devices with a cash acceptance function.
5. Always check with the loan officer the date of crediting funds to the account (in the case of a cashless transfer) and the date of repayment of your loan. Money or wiring may "hang".
6. If you plan to repay the entire amount of the loan debt ahead of schedule, it is advisable to personally come to the bank, ask for a document confirming the balance of the loan debt with interest on the current date, and only then repay the loan. Do not call the bank by phone to find out the balance of the debt, and do not repay the loan through the terminal without receiving written confirmation from the bank - not all banks are "bona fide".
7. At the final repayment of the loan, keep all documentation confirming this fact. It can be useful in case of possible misunderstandings.
VI. Conclusion.
So what are the benefits of a mortgage? :
1. The first and most important plus is that housing purchased with a mortgage loan immediately becomes your property, so immediately after receiving the documents you can prepare for a housewarming.
2. The price of real estate is constantly growing, and at a catastrophic rate, the growth of inflation "eats" the value of money, so the option of accumulation "disappears", respectively - buying an apartment with a mortgage loan is a smart investment.
3. Another “plus” is that if, by a happy coincidence, there is a possibility of early repayment of a mortgage loan, then you will not face penalties and you can easily repay in full or in part at any time, and interest will be charged on the remaining loan amount.
4. Again, the rent for an apartment is quite comparable to the monthly payments on the loan, only in the latter case you pay for your own.
5. If after some time interest rates on a mortgage loan for real estate decrease, it is possible to transfer the loan to another bank (refinancing).
Cons of a mortgage loan:
1. An initial fee. now this required condition to obtain bank approval, and this is not a lot, not a little, almost 15-20% of the cost. Although, if you fall under the Affordable Housing Federal Target Program, a way out has been found! True, you will have to run around the authorities, but it's worth it. How can you tell if you fit or not? Everything is very simple: a married couple is recognized as a young family, where the age does not exceed 35 years.
2. A huge overpayment on the interest of the loan, we can say 100 percent.
3. High official incomes are required, moreover, documented ones (personal income tax certificate-2).
4. Well, the last "minus" - after all, a mortgage loan is a moral obligation, and a feeling of discomfort is possible, but it is quickly compensated by the fact that you have your own housing.
In general, if you want to buy a home, and at the same time have a stable income, the loan option should be considered. And having received a loan, you should monitor market interest rates in order to refinance.
Everyone has to find the perfect compromise between the advantages and disadvantages of a mortgage. Today, the choice of banks and their mortgage programs wide enough, and anyone who wants to solve their housing problems with the help of a mortgage can choose a worthy partner
Bibliography.
1. I. V Lipsitz. Economy without secrets. - M., 2006.
2. Dorofeev V.G., Kuznetsova L.V., Minaeva S.S., Suvorova S.V. The study of interest in basic school // mathematics at school. - 2002. - No. 1.
3. A.S. Simonov Interest and banking // Mathematics at school. 1998. No. 4
4. I. L. Brodsky, A.M. Vidus, A.B. Korotaev. Collection of text problems in mathematics for specialized classes./ Pod. Ed. I. L. Brodsky. - M.: ARKTI, 2004.
5. G.V. Dorofeev, L.G. Peterson Mathematics 6th grade. Part 1. - M.: Yuventa Publishing House, 2006.
Application No. 1.
Target program "Improvement of living conditions of the population of Khanty-Mansi Autonomous Okrug - Ugra for 2011 - 2013 and for the period up to 2015", according to
Who can buy housing under the target program:
Citizens residing on the territory of the Autonomous Okrug;
Those in need of better housing conditions (the provision of housing is less than 12 sq.m. per family member);
o Citizens leaving KhMAO-Yugra for subjects of the Russian Federation that do not belong to the regions of the Far North and equivalent areas;
o Disabled people of groups I and II, disabled since childhood, families with disabled children, permanently residing in the Autonomous Okrug for at least 10 years;
o Old-age pensioners permanently residing on the territory of the Autonomous Okrug, having a total length of service in the Autonomous Okrug of at least 15 calendar years.
o Citizens leaving the settlement, which is closed in accordance with the decision of the state authorities of the Autonomous Okrug;
o Citizens who moved in before 1995 in premises (beams, wagons) located within the boundaries of the settlements of the Autonomous Okrug and not classified as residential premises.
Terms of participation in the program:
o Lack of residential premises in other subjects of the Russian Federation;
o Not receiving housing subsidies;
o There is no need to improve living conditions in the Autonomous Okrug.
o Subsidy for the payment of a contract for the acquisition (construction) of a dwelling in the amount of 30% of the estimated cost of the dwelling.
o Young family (including those consisting of one young parent), regardless of the presence of children. At the same time, the age of each young parent should not exceed 35 years.
Terms of participation in the program:
Forms of state support:
o Subsidy in the amount of the cost of 12 square meters per child.
o Citizens from among the indigenous peoples of Khanty-Mansi Autonomous Okrug-Yugra
Terms of participation in the program:
o Need for better living conditions. Security less than 12 sq.m. total living area per family member.
Forms of state support:
o Compensation of the interest rate on the loan (part of the loan) in the amount of up to 2 million rubles. up to 20 years;
o A subsidy in the amount of 100% of the estimated cost of the purchased housing according to the norms
o State civil servants of the Autonomous Okrug, municipal employees of the Autonomous Okrug, employees of municipal institutions of the Autonomous Okrug, employees of other bodies, whose financial support is fully funded from the budgets of the municipalities of the Autonomous Okrug.
Terms of participation in the program:
o Need for better living conditions. Security less than 12 sq.m. total living area per family member.
Forms of state support:
o Compensation of the interest rate on the loan (part of the loan) in the amount of up to 2 million rubles. up to 20 years old.
· Employees
· Employees who carry out other activities in the state authorities of the Autonomous Okrug, employees of other bodies, the financial support of which is fully carried out at the expense of the budget of the Autonomous Okrug.
Terms of participation in the program:
Forms of state support:
· Subsidy in the amount of up to 70% of the cost of purchased housing.
The waiting list.
· Citizens who are registered with the local self-government bodies of the municipalities of the Khanty-Mansiysk Autonomous Okrug - Yugra as in need of housing provided under a social contract of employment.
Terms of participation in the program:
· The applicant must be registered at the place of permanent residence as in need of housing provided under a social contract of employment.
Forms of state support:
· Compensation of the interest rate on the loan (part of the loan) in the amount of up to 2 million rubles. up to 20 years;
· A subsidy in the amount of 30% of the cost of purchased housing according to the standard for family composition.
Citizens living in adapted premises
· Citizens who moved in before 1995 in premises adapted for living (beams and wagons).
Terms of participation in the program:
· Lack of residential premises in the property or under a social contract of employment in the territory of the Russian Federation.
Forms of state support:
· Compensation of the interest rate on the loan (part of the loan) in the amount of up to 2 million rubles. up to 20 years;
A subsidy in the amount of 30% of the estimated cost of purchased housing according to the standard for family composition. Shareholders
· Citizens affected by the actions (inaction) of developers on the territory of the Autonomous Okrug.
Terms of participation in the program:
The presence of a citizen of the contract of participation in shared construction concluded in accordance with federal law dated December 30, 2004 No. 214-FZ;
Degree of completion of construction in progress apartment building is at least 70%.
Forms of state support:
· Compensation of the interest rate on credits (loans) in the amount of up to 500 thousand rubles;
· Compensation of a part of the cost of the object - 70% of the cost of the equity participation agreement.
Other citizens.
Citizens wishing to acquire residential premises in the property.
Terms of participation in the program:
Need for better living conditions. Security less than 12 sq.m. total living area per family member.
Forms of state support:
· Compensation of the interest rate on the loan (part of the loan) in the amount of up to 2 million rubles. up to 5 years.
RF. 646020. Omsk region, Isilkul district, Isilkul, st. Soviet 2a,
tel. 20 - 903, email. address: schkola 3_isil [email protected] mail. en
Mathematics in percentages and credits.
Completed by: Elizaveta Kozlova, 9th grade student.
Head: Zinchenko Elena Vladimirovna, teacher
mathematics and computer science
2013
Introduction…………………………………………………….3
The history of the emergence of interest…………………………5
Tasks for calculating compound interest……………………6
Tasks for bank interest ………………………..9
Experimental work…………………….11
Conclusion……………………………………………….13
References………………………………………14
Introduction.
Relevance of the topic:
In our time, in almost all areas of human activity, there are percentages. Therefore, the topic I have chosen is especially relevant.
The concept of "percentage" cannot be dispensed with in any accounting, nor in financial analysis, nor in statistics. To calculate the salary of an employee, you need to know the percentage of tax deductions; in order to open a deposit account in a savings bank, our parents are interested in the amount of interest on the amount of the deposit; to know the approximate rise in prices in the coming year, we are interested in the percentage of inflation. It is in trade that the concept of "interest" is used most often: discounts, markups, markdowns, profits, loans, income tax, etc. All of these are percentages.
The purpose of this work:
Show the breadth of interest and explore their use in lending, find out which loan is more profitable.
To achieve this goal, you need to do the following tasks:
- analyze the literature on the topic "Percentage and percentage calculations";
- Familiarize yourself with the compound interest formula
- show the reception of the acquired knowledge in lending (consumer credit).
Solving mathematical problems of practical content makes it possible to be convinced of the importance of mathematics for various spheres of human activity, to see the breadth of possible applications of mathematics, to understand its role in modern life.
Ability to perform interest calculations necessary for every person. Therefore, the plots of the tasks are taken from real life. Various types of lending are considered.
The value of the results obtained is that they demonstrated a wide range of applications of interest calculation in economic areas, that is, a close relationship between mathematics and economics.
History of interest.
The word "percentage" is of Latin origin: "pro centum" is "from a hundred." Often, this phrase is used instead of the word "percentage". That is, a hundredth of a number is called a percentage.
Interest was known to the Indians as early as the 5th century. and this is obvious, since it was in India that for a long time the account was kept in the decimal number system.
Interest was especially common in ancient Rome. The Romans called interest the money that the debtor paid to the lender for every hundred.
The Romans took interest from the debtor (i.e., money in excess of what was lent). At the same time, they said: "for every 100 sesterces of debt, pay 16 sesterces of interest." It can be called the first loan in the world.
From the Romans, interest passed to other peoples of Europe.
In Europe, decimal fractions appeared 1000 years later, they were introduced by the Belgian scientist Simon Stevin. In 1584 he first published a table of percentages.
The introduction of percentages was convenient for determining the content of one substance in another; as a percentage began to measure the quantitative change in the production of goods, the rise and fall of prices, the growth of money income, etc.
Symbol did not appear immediately. First they wrote the word "hundred" like this: cto.
In 1685 in Paris, the book "Guide to commercial arithmetic" was printed, where by mistake instead of cto was typed. After that, the sign received universal recognition and we still use this percent sign.
Compound interest problem:
The price of 51.2 rubles for a capillary pen was increased three times by the same percentage, and then decreased three times by the same percentage. As a result, the price of the pen was 21.6 rubles. By what percentage did you increase and then decrease the price of a capillary pen?
Let's try to calculate, using the given numbers, by how many percent they increased and then reduced the price of a capillary pen. This is a compound interest problem. Compound interest is calculated using the formula:
or ,
where a is the initial value of some quantity;
To- the value that resulted from several changes in the initial value;
n is the number of changes in the initial value;
R- percent change.
The plus sign is used in problems when calculating an increase in the price of a product, and the minus sign is used when calculating a price decrease.
Indeed, if changing the number to R% replace by multiplying by the desired number, then, increasing the number a on the R%, we get .
That is, to increase the number by R% , it is enough to multiply it by , and to reduce the number by R%, just multiply it by
Decision: Let us return to the problem and from the condition of the problem we have
or .
;
; R=50
Answer: The price of a capillary pen has increased and decreased by 50%.
Consider a few more problems on the application of the compound interest formula:
Task 1. ( from data of the Savings Bank of Russia) the depositor put a certain amount on the Molodezhny deposit in the Savings Bank of Russia. Two years later, the contribution reached 2809 rubles. What was the initial contribution at 6% per annum?
Decision :
Let be X rubles - the initial contribution.
X(1+6 0.01) 2 =2809
1,06 2 X=2809
1,1236X=2809
X=2500
Answer: the initial contribution was 2500 rubles.
Task 2 .(from the exam) The price of a Volga car was reduced first by 20%, and then by another 15%. At the same time, it began to cost 238,000 rubles. What is the original price of the car?
Decision:
Let be X rubles will be the initial cost of the car.
X(1-0.2) (1-0.15)=238000
X 0.8 0.85=238000
X 0.68=238000
x= 350000
Answer: 350,000 rubles - the initial cost of the car.
Task 3. The speed of a body moving with uniform acceleration increases by 10% every second. His current speed is 10 m/s. What will be its speed in three seconds?
Decision:
(m/s)
Answer: in three seconds the speed will be 13.31 m/s.
Task 4: After a price reduction of 30%, the sweater began to cost 2100 rubles. How much was the sweater before the price cut?
Solutions:
Using the diagrams, we get that
S o ∙ (1-30 ∙ 0.01)=2100
S about ∙0.7=2100;
S o =3000
3000 (rubles) - the sweater cost before the price reduction.
Answer: 3000 rubles.
Tasks for bank interest.
Loan in the amount of 500,000 rubles. issued for a period of 5 years at 7% per annum. Compound interest is accrued, the frequency of accrual is at the end of each year. Determine the total amount owed on the loan at the time of repayment.
Decision.
(rub.)
Answer: the amount of debt at the time of repayment is 701,275.87 rubles.
A loan for buying a house was issued in the amount of 4,000,000 rubles for a period of 5 years. The interest rate is 14% per annum. The loan is repaid at the end of each month. Determine the amount to be paid for all five years and the monthly repayment.
Decision.
This problem is solved using the compound interest formula with interest accrued several times a year: ( n - credit term, m - number of payments per year). Then (rub.) In this case, the monthly payment will be (rub.).
Answer: the amount to be paid for all five years is 8.022 10 6 rubles and the monthly repayment payment is 133.7 10 3 rubles.
Loan in the amount of 200,000 rubles. issued for a period of 5 years. The nominal annual rate is 20% per annum. Compound interest is accrued, the frequency of accrual is at the end of each quarter. Determine the total amount owed on the loan at the time of repayment.
Decision.
, n = 5, and m = 4. (rub.)
Answer: the amount of debt at the time of repayment is 530,660 rubles.
On January 1, the depositor deposited 2,000 rubles in a bank account under the ordinary interest scheme and an approximate number of days at 22% per annum. By what number do you need to make a deposit in order to receive 2350 rubles?
Decision.
The duration of the year according to the scheme is approximate, the number of days will be 360. Let's transform the formula of one-time intra-annual accruals in such a way as to highlight the number of days of a financial transaction: ; (days), i.e. 286 days = 30 9 + 16 days.
Answer. The deposit must be made for 9 months and 16 days, that is, until October 16.
Experimental work.
Consider a practical problem that has application in real life - this is the calculation of loans. Nowadays, people more and more often take goods on credit (a loan in cash or commodity form, provided by the lender to the borrower on a repayment basis, most often with the payment of interest for using the loan), which is available to everyone.
Of course, everyone wants to buy the right product, as profitable as possible. It is very interesting which loans in our city are the most convenient. To conduct this experiment, I considered consumer loans from banks, in which teachers of our school receive wages, Rosbank and Sberbank. In order to calculate the final loan amount, you cannot do without compound interest formulas.
Transforming the formula, we get:
where a- the initial cost of the loan;
s is the term of the loan;
R- annual interest rate;
m — number of days in a year (360 days, each month - 30 days)
Suppose we need to purchase goods in the amount of 30,000 rubles and pay for it within 6 months.
Sberbank of Russia
The loan amount should not exceed your income multiplied by 10.
unsecured consumer loan(up to RR 1,500,000), rate - 17-25.5% up to 5 years.
Let's calculate our credit. rubles, i.e. the overpayment will be 2550 rubles.
consumer credit guaranteed by individuals(up to RR 3,000,000), rate - 16.5 - 24.5% up to 5 years.
rubles, i.e. overpayment - 2475 rubles. This loan is profitable to take, but reliable guarantors are needed.
Rosbank
consumer credit "Just money"(from 18,000 to 40,000 RR) rubles, overpayment - 2760 rubles.
rubles, overpayment - 3060 rubles.
It can be seen from the calculations that it is more profitable to take a loan of 30,000 RR for 6 months at Sberbank, and a loan for a large amount and a long term - at Rosbank. But in this work, we do not take into account the nuances that may be when obtaining loans, banks will tell you in detail about this.
Knowing the compound interest formula, it is easy to calculate the benefit of a loan at any time. This helps to save the family budget.
Conclusion.
In conclusion, I would like to say that the ability to perform percentage calculations and calculations is necessary for every person, since we constantly encounter percentages in everyday life. Hope my work finds practical use not only in algebra lessons and in preparing for exams, but will also help in life after school, even if the future profession will not be related to mathematics. :// sberbank . en - website of Sberbank of Russia
http :// rosbank . en - Rosbank website
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