Compound interest is used in cases where interest on loans (loans) is not paid immediately, but is added to the amount of debt with the subsequent determination of the accrued amount of FV. This “interest on interest” calculation procedure is called capitalization. The compounding rate increases in geometric progression, and the compounding (accumulation) process is described by the equation FV= PV(1+i)n

In this regard, the following formula is used to calculate the percentage amount:

where i is the annual rate;

n - number of accrual periods;

m - number of accrual periods;

n*m - total number of the accrual period.

When the intervals between successive payments are constant, then such a sequence is called financial rent or annuity. An annuity (a series of equal payments over n periods) is called ordinary if payments are made at the end of each period, and advance if payments are made at the beginning of each period.

The first function of compound interest is the accumulated amount of capital. We have already seen that, unlike simple interest, compound interest assumes that income is generated not only by the initial amount, but also by the interest previously received on it. To determine the value that capital will have in a few years FV when using the compound interest procedure, use a formula reflecting the process of accumulation (compounding), growth in accordance with a geometric progression: FV= PV(1+i)n

where FV is the accumulated (future) amount of capital;

PV - current value (cost of investment in the initial period);

i - interest rate (for example, i = 0.10, i.e. 10%);

n - number of accrual periods.

This formula in financial and economic calculations determines the first function of compound interest, and the expression (1+i)n called the multiplier (coefficient) of the increase or the future value of a unit of accumulated capital F 1: F 1 = (1+i)n

where F 1 is calculated or determined from the compound interest table.

Thus, the process of accumulating deposited or invested capital is the process of accumulating money at a given rate i over a certain period of time p.

If accumulation is more frequent than once a year, the actual income received at the end of the year includes interest accrued during the year. In this regard, a distinction is made between annual nominal and annual actual (effective) interest rates.

Annual actual rate is the annual rate taking into account compounded interest. The annual actual rate is calculated as a percentage of income to capital at the end of the year, to the amount of capital at the beginning of the year; in practice, the actual rate is called effective.

The second function of compound interest is the future value of a n-period annuity. Let's consider a series of equal and uniform payments (deposits) at interest for a certain number of periods, while in each period capital deposits (RMT) of the same amount are made (a series of deposits - an annuity). This flow of payments is annuity.

The accumulated amount of an annuity (n-period annuity) is the sum of all members of the annuity with interest accrued on them by the end of its term.

An annuity is called ordinary, if payments are made at the end of each period (post-numerando annuity), and advance, if payments are made at the beginning of each period (pre-numerando annuity).

The accrued amount of annuity for an n-period annuity will be equal to:

where (1 + i) n – 1/f = F 2 is the second function of compound interest.

In financial calculations, the latter expression is also called the accumulation fund factor or the future value of a n-period annuity with a payment of one monetary unit (see Inwood's compound interest table).

Unlike a regular annuity, with an advance annuity (prenumerando), the first payment is made at the beginning of the first period, i.e. it generates income during all n-periods. Each subsequent payment works one period less than the previous one, finally, the last payment generates income for only one period. As with an ordinary annuity, the future values ​​of each payment form a geometric progression with the denominator (1 + i), and the first term of this progression is PMT(1 + i). Using the formula for calculating the sum and terms of a geometric progression, we obtain:

In this case, the accumulation fund factor F 2 (the future value of the advance annuity with a payment of one monetary unit) will be equal to:

The third function of compound interest (reverse second) - capital replacement fund factor. From the second function we have:

Where i/ (1+i)n –1= F 3 - compensation fund factor, third function of the complex

percent.

Coefficient F 3 shows the amount of money that must be deposited at the end of each period so that after a certain number of periods the account balance is one monetary unit; Moreover, this factor takes into account the interest received on contributions.

You can compare the accumulation fund factor F 2 and the compensation fund factor F 3. It can be seen that the function F 3 for fixed n and i is the inverse of the accumulation fund factor F 2 i.e.

Comparing the accumulation fund factor (the future value of an advance annuity with a payment of one unit) and the advance compensation fund factor, we obtain the ratio:

The fourth function of compound interest (the inverse of the first) is the present value of a future cash flow, i.e. the current value of money (investments), PV is determined from the expression:

Where 1/ (1+i)n= F 4 - the fourth function of compound interest, the current value of a future unit.

Comparing the resulting formula with the factor of the first function, we see:

The process of recalculating the future value of a sum of money (cash flow); FV is now called discounting, and the rate at which discounting is carried out is often called the discount rate.

Using the function F. two questions can be answered:

1. How much will the amount that the investor receives after l-periods be worth today?

2. How much should you buy an object for (how much should you invest in the object) in order to ensure the required rate of income as a result of its future sale after n-periods?

The fifth function of compound interest is the present value of an annuity. Like the previous one, this function is associated with the discounting process. The fifth function determines the current value of a series of uniform equal cash receipts over n-periods, taking into account a given amount. The current value of the payment flow PV is the sum of all its members (annuities), reduced (discounted) by the interest rate at a specific point in time. The present value can be an ordinary annuity or an advance n-period annuity

where PV is the sum of the i terms of a geometric progression with the denominator 1/1+i and the first term PMT/1+c

From here, using the well-known formula for the sum of terms of a geometric progression, we obtain the equation:

Where1 – (1+i)n/ i= F 5 - the fifth function of compound interest, the current value of an ordinary annuity.

An advance annuity is structured so that the first payment of RMT 1 in the income stream is made immediately, and subsequent payments are made at regular intervals. Since RMT 1 is produced at the initial moment of time, there is no need to discount it. The subsequent i - 1 payment and others are discounted taking into account the fact that the kth payment is made after k - 1 periods from the initial moment.

In this case, the sum of the cost of all n-payments is

geometric progression with denominator 1/1+i and first term PMT.

Then the present value of the advance annuity will be equal to:

If RMT = 1, then we obtain an expression for the factor of the current value of the advance annuity F" 5:

The functions F 5 and F " 5 are of particular importance in statistical calculations, in the assessment of investment projects, and income-generating property.

The sixth function of compound interest (reverse to the 5th) in the practice of economic and financial calculations is called the mortgage constant, or the amount of payments to cover the debt. Based on the known current value (loan size), the size of payments is determined:

For PV = 1, we obtain the value of the contribution to the depreciation of the monetary unit - this is the sixth function of compound interest - F 6 (mortgage constant).

For ordinary contributions (post-numerando annuity), the sixth function has the form:

For advance payments (renta prenumerando), the sixth function has the form:

Each equal installment of RMT includes the amount of interest money I nt and payment of the initial amount PRN - the amount of the principal debt: RMT = PRN +Int

It should be emphasized that the mortgage constant function F 6 is related to function F 3 as follows: F 6 =F 3 +i those . mortgage permanent is a contribution to capital depreciation equal to the sum of the compensation fund factor F 3 and the interest rate on capital i.

Equal-annuity method of return of fixed assets (Inwood method). RMT payments are made at the end of the period in equal shares with increasing amounts of PRN for the return of the principal amount of debt and with decreasing accruals of interest i - income.

Uniformly rectilinear method (Ring's method). Net operating income decreases uniformly at a constant rate of return of principal PRN, and income I nt decreases uniformly. Unlike Ring's method, Inwood's method is based on the fact that the mortgage constant is equal to the sum of the recovery fund factor F 3 and the capitalization rate i.

Sixth function compound interest is widely used in the economic justification of leasing operations.

So, to determine the value of income-producing property, it is necessary to determine the current value of the money that will be received some time in the future.

It is known, and in conditions of inflation it is much more obvious, that money changes its value over time. The main operations that make it possible to compare money at different times are the operations of accumulation (increase) and discounting.

Accumulation is the process of reducing the current value of money to its future value, provided that the invested amount is held in an account for a certain time, earning periodically compounded interest.

Discounting is the process of reducing cash flows from investments to their current value.

In valuation, these financial calculations are based on a complex process in which each subsequent calculation of the interest rate is carried out on both the principal amount and the unpaid interest accrued for previous periods.

A total of six functions of the monetary unit based on compound interest are considered. To simplify calculations, tables of six functions have been developed for known rates of income and the accumulation period (I and n); in addition, you can use a financial calculator to calculate the required value.

1 function: Future value of a monetary unit (accumulated amount of a monetary unit), (fvf, i, n).

If accruals are made more often than once a year, then the formula is converted to the following:

k– frequency of accumulations per year.

This function is used when the current value of money is known and it is necessary to determine the future value of a monetary unit at a known rate of income at the end of a certain period (n).

Forex classes are a wonderful way for you to prepare for successful work on the international Forex currency market!

Rule of 72x

To approximately determine the period for doubling capital (in years), it is necessary to divide 72 by the integer value of the annual rate of return on capital. The rule applies to rates from 3 to 18%.

A typical example for the future value of a monetary unit would be a problem.

Determine what amount will be accumulated in the account by the end of the 3rd

year, if today you put it into an account that brings 10% per annum, 10,000

FV=10000[(1+0.1) 3 ]=13310.

2 function : Current value of the unit (current value of reversion (resale)), (pvf, i, n).

The current value of a unit is the inverse of its future value.

If interest is calculated more often than once a year, then

An example of a problem is the following: How much should be invested today in order to get 8,000 in the account by the end of the 5th year, if the annual rate of return is 10%.

3 function : Present value of the annuity (pvaf, i, n).

An annuity is a series of equal payments (receipts) spaced from each other by the same period of time.

There are ordinary and advance annuities. If payments are made at the end of each period, then the annuity is ordinary; if at the beginning, it is an advance annuity.

The formula for the present value of an ordinary annuity is:

PMT – equal periodic payments. If the frequency of accruals exceeds 1 time per year, then

Formula for the present value of an advance annuity:

Typical example:

The rental agreement for the dacha is for 1 year. Payments are made monthly in the amount of 1000 rubles. Determine the current value of lease payments at a 12% discount rate if a) payments are made at the end of the month; b) payments are made at the beginning of each month.

4 function : Accumulation of a monetary unit for a period (fvfa, i, n).

As a result of using this function, the future value of a series of equal periodic payments (receipts) is determined.

Payments can also be made at the beginning and end of the period.

Ordinary annuity formula:

Typical example:

Determine the amount that will be accumulated in an account yielding 12% per annum by the end of the 5th year, if 10,000 rubles are annually deposited into the account a) at the end of each year; b) at the beginning of each year.

5 function : Contribution to depreciation of a monetary unit (iaof, i, n) The function is the inverse of the present value of an ordinary annuity. The contribution to the depreciation of a monetary unit is used to determine the amount of the annuity payment to repay a loan issued for a certain period at a given loan rate.

Amortization is a process defined by this function that includes interest on the loan and payment of the principal amount.

For payments made more often than once a year, the following formula is used:

An example is the following task: Determine what payments should be in order to repay a loan of 100,000 rubles issued at 15% per annum by the end of the 7th year.

6 function : Compensation fund factor (sff, i, n)

This function is the inverse of the function of accumulating a unit over a period. The recovery fund factor shows the annuity payment that must be deposited at a given percentage at the end of each period in order to receive the required amount after a given number of periods.

To determine the amount of payment, the formula is used:

For payments (receipts) made more often than once a year:

An example would be a task.

Determine what payments should be in order to have 100,000 rubles in an account earning 12% per annum by the end of the 5th year. Payments are made at the end of each year.

The annuity payment defined by this function includes payment of the principal amount without payment of interest.

Six functions of compound interest can be used in real estate valuations. The accumulated amount of the unit allows you to answer the question: “How much can the property be sold for based on its current market value and the expected growth of the latter using compound interest?” The accumulation of one unit over a period shows how regular deposits will grow at compound interest. The recovery fund factor shows how much money must be deposited periodically in order to accumulate $1 over a certain number of compounding periods. It shows what the annual rate required to recover the investment in a given asset should be.

The present value of a unit shows the present value of a sum of money to be received in a lump sum in the future, such as from the expected sale of land. The annuity factor shows the value of a cash flow, such as income from a rental property or mortgage payments. The unit amortization contribution factor determines the size of the periodic payment required to amortize the loan, including interest and principal payments.

Each of the six functions is based on compound interest, which means that the entire principal amount held in the deposit account must earn interest, including interest remaining in the account from previous periods. Moreover, interest is paid only on the funds in the deposit account, and not on interest or principal withdrawn from it.

The six compound interest functions can be used to solve almost all arithmetic problems associated with valuing income-producing real estate properties.

Money has a time value, i.e. A ruble received today is worth more than a ruble received tomorrow. And not only because inflation can reduce its purchasing power, but also because a ruble invested today will bring concrete profit tomorrow. The time value of money is an important aspect when making decisions in financial practice in general and when evaluating investments in particular.

Calculation based on compound (cumulative) interest means that the interest accrued on the initial amount is added to it, and interest is accrued in subsequent periods on the already accrued amount. The process of capital accumulation in this case occurs with acceleration. It is described by a geometric progression. The mechanism for increasing the initial amount (capital) using compound interest is called capitalization. In financial and economic terms, capitalization is defined as the rate of return on invested capital. When assessing real estate and investments, this term takes on a slightly different meaning.

There are annual capitalization (the interest payment is calculated and added to the previously increased amount at the end of the year), semi-annual, quarterly, monthly and daily. There is also the concept of continuous compounding, which in its meaning is very close to daily compounding.

The calculation of the accrued amount at compound interest is carried out using the formula:

cash payment rent debt

where S is the accumulated amount;

P - the initial amount on which interest is calculated;

i - compound interest rate, expressed as a decimal fraction;

n is the number of years during which interest accrues.

The value is called the compound interest multiplier. It shows how much one monetary unit will increase when interest increases on it at rate i for n years.

However, in most cases, it is not the quarterly or monthly rate that is indicated, but the annual rate, which is called the nominal rate. In addition, the number of periods (t) of interest accrual per year is indicated. Then the formula is used to calculate the accrued amount:

where i is the nominal annual interest rate;

t - the number of interest calculation periods per year;

n - number of years;

tp - the number of interest periods for the entire term of the contract.

Using formulas (3.1) and (3.2), we carried out a discrete increase in interest, i.e. interest was accrued annually, quarterly or monthly. Continuous compounding means that interest is compounded over the shortest possible period of time. Although it is understood that this period will be infinitely short, the most accurate approximation of continuous compounding is daily compounding. In this case, formula (3.2) can be used to determine the accumulated amount. So, with an annual rate of 10% and a year length of 360 days (a similar year length is accepted in banking calculations in a number of countries) with daily interest accrual.

The term “discounting” is used very widely in financial practice. It can be understood as a method of finding the value P at a certain point in time, provided that in the future, when interest is calculated on it, it could amount to the accrued amount S. The value P, found by discounting the accrued value S, is called the modern, current or reduced value. With the help of discounting, the time factor is taken into account in financial calculations. The current value is the reciprocal of the accumulated value, i.e. Discounting and the discount rate are opposite to the concepts of “accumulation” and “interest rate”. For example, if in a year you should receive 1,100 rubles from your bank deposit, and the bank accrued at the rate of 10% per annum, then the current value of your deposit is 1 thousand rubles.

Since the current value is the reciprocal of the accumulated amount, it is determined by the formula:

where is the discount factor. It shows the present value of one monetary unit that is to be received in the future.

When interest is calculated th times a year, the current value is calculated using the formula:

where is the discount factor.

When considering a modern value, it is necessary to pay attention to two of its properties. One of them is that the interest rate at which discounting is carried out and the modern value are inversely related, i.e. the higher the interest rate, the lower the current value, other things being equal.

Also, the current value and payment term are inversely related. As the payment term (p) increases, the current value will become less and less. The limit of values ​​of the modern value (P) with the payment term (p) tending to infinity will be:

With very long payment terms, its current value will be extremely insignificant. So, for example, if someone decides to bequeath to his descendants to receive an amount of 50 million rubles in 100 years, then for this he just needs to put 22.72 thousand rubles at 8% per annum.

With an increase in the value t (the number of interest periods), the discount factor decreases, and therefore the current value P decreases.

Meanwhile, payment for concluded transactions may include either a one-time payment or a series of payments distributed over time. Payment of rent, payments for purchased property in installments, investment of funds in various programs, etc. in most cases provide for payments to be made at certain intervals, i.e. a flow of payments is formed.

A series of consecutive fixed payments made at regular intervals is called financial rent, or annuity.

According to the moment of payments of annuity members, the latter are divided into ordinary (post-numerando), in which payments are made at the end of the corresponding periods (year, half-year, etc.), and pre-numerando, in which payments are made at the beginning of these periods. There are also annuities that provide for the receipt of payments in the middle of the period.

General indicators of annuity are: the accumulated amount and the modern (current, reduced) value.

The accrued amount is the sum of all members of the payment stream with interest accrued on them at the end of the term, i.e. on the date of the last payment. The accrued amount shows how much the capital will represent when contributed at regular intervals throughout the entire annuity term along with accrued interest.

The current value of the payment flow is the sum of all its members, reduced (discounted) by the interest rate at a certain point in time, coinciding with the beginning of the payment flow or preceding it.

The value is the annuity growth coefficient, which is also called the coefficient of accumulation of a monetary unit for the period.

It was previously stated that some annuities are realized immediately after the contract is concluded, i.e. The first payment is made immediately and subsequent payments are made at regular intervals. Such annuities (prenumerandos) are also called advance or entitlement annuities. The sum of the members of such an annuity is calculated by the formula:

That is, the sum of the annuity terms prenumerando is greater than the accumulated sum of the annuity postnumerando by a factor, therefore the accumulated sum of the annuity prenumerando is equal to:

where S is the accumulated postnumerando sum.

In cases where payments are made in the middle of periods, the accrued amount is calculated using the formula:

where S 0 is the accrued amount of payments paid at the end of each period (post-numerando annuity).

The modern value of the annuity (also called the current or reduced value) is the sum of all terms of the annuity, discounted at the time of reduction at the selected discount rate. For rent with terms equal to R, the modern value is calculated using the formula:

where A is the rent reduction coefficient, showing how many rent payments (R) are contained in the modern value;

i is the annual interest rate at which discounting is carried out;

n is the period of rent payments.

This figure is also called the present value of an ordinary annuity, or the present value of future payments. Rent reduction coefficients are tabulated.

Costs associated with debt repayment, i.e. repaying the amount of the debt itself (debt amortization), and paying interest on it, are called debt service costs.

There are various ways to pay off debt. The parties to the transaction stipulate them when concluding the contract. In accordance with the terms of the contract, a debt repayment plan is drawn up.

One of the most important elements of the plan is determining the number of payments during the year, i.e. clarification of the number of so-called urgent payments and their magnitude.

Urgent payments are considered as funds intended to repay both the principal debt and current interest payments on it. In this case, the funds used to repay (amortize) the principal debt may be equal or vary according to some laws, and interest may be paid separately.

Debt can be repaid by annuities, i.e. payments made at regular intervals and containing both payment of principal and interest on it. The amount of the annuity can be constant, or it can change in arithmetic or geometric progression.

Below we will consider the case when the plan is drawn up in such a way that the loan is repaid at the end of each billing period in equal urgent payments, including payment of the principal amount of the debt and interest on it and allowing the loan to be fully repaid within the specified period. Each urgent payment (Y) will be the sum of two quantities: the annual cost of repaying the principal debt (R) and the interest payment on it (I), i.e.

The calculation of the urgent annual payment is made using the formula:

where i is the interest rate;

n - loan term;

D is the amount of debt.

The value is called the debt repayment ratio, or the contribution to the depreciation of the monetary unit. It can also be thought of as the inverse of the present value of the annuity, i.e. .

In practice, it may be necessary to know the amount of the outstanding principal balance for any period. This value is calculated by the formula:

where k is the number of the billing period in which the last urgent payment was made.

Buying real estate in most cases involves obtaining a loan. In this regard, it is necessary to know in advance how much you will need to deposit each payment period in order to ensure that the principal amount of the debt (excluding interest payments) is repaid on time.

To solve this problem we use the formula:

where R 1 is the cost of repaying the principal debt in the first payment period;

D is the amount of the principal debt;

n - loan term;

i - interest rate.

The value is called the compensation fund factor. It shows how much will need to be deposited at the end of each payment period so that the principal loan amount will be fully repaid within a specified number of periods.

To calculate the amount used to repay the principal debt in any period, it is necessary to multiply the compensation fund factor and the compound interest multiplier for a given period, i.e.

where k is the number of periods for which the principal debt was repaid.

We examined the functions of compound interest using the basic formula that describes the accumulated amount of a unit. All considered formulas (factors) are derived from the main formula. Each of them provides that the money in the deposit account earns interest only as long as it remains in that account. Each of the formulas takes into account the effect of compound interest, i.e. that interest which, when received, is converted into the principal amount.

All of the above formulas are summarized in a table, which makes financial calculations somewhat easier. The table has the name: “Tables of compound interest. 6 functions of compound interest. The quantities included in the table are in a certain relationship with each other. Below in the table. this connection is given.

6 FUNCTIONS OF MONETARY UNIT. COMPOUND INTEREST FORMULAS

The theory of changes in the value of money is based on the assumption that money, being a specific product, over time change their value and, as a rule, depreciate. Changes in the value of money occur under the influence of a number of factors, the most important of which are inflation and the ability of money to generate income, provided they are wisely invested in alternative projects. The main operations that make it possible to compare money at different times are the operations of accumulation (increase) and discounting.

TERMS AND DEFINITIONS

Accumulation is the process of reducing the current value of money to its future value, provided that the invested amount is held in an account for a certain time, earning periodically compounded interest.

Discounting is the process of reducing cash flows from investments to their current value.

Annuity payments (PMT) is a series of equal payments (receipts) spaced from each other by the same period of time. Highlight If payments are made at the end of each period, then the annuity is ordinary; if at the beginning, it is an advance annuity.

Current value(PV)(English: Present value) - the original amount of debt or an estimate of the current value of a sum of money, the receipt of which is expected in the future, in terms of an earlier point in time.

Future Value (FV)(eng. Future value) - the amount of debt with accrued interest at the end of the term.

Rate of return or interest rate (i)(eng. Rate of interest) - is a relative indicator of investment efficiency (rate of return), characterizing the rate of increase in value over the period.

Debt repayment period (n)(eng. Number of periods) - the time interval after which the amount of debt and interest must be repaid. The term is measured by the number of billing periods, usually equal in length (for example, month, quarter, year), at the end of which interest is accrued regularly.

Frequency of savings per year (k) - frequency of interest calculation influences the amount of accumulation. The more often interest is calculated, the greater the accumulated amount.

NOTATION FOR FORMULAS

FV – future value of a monetary unit;

PV – current value of a monetary unit;

PMT – equal periodic payments;

i – income rate or interest rate;

n – number of accumulation periods, in years;

k – frequency of accumulations per year.

6 FUNCTIONS OF MONETARY UNIT

Compound interest formula - 1 function

Future value of a monetary unit ( FV) – accumulated amount of a monetary unit. The accumulated amount of a monetary unit shows how much a monetary unit invested today will amount to after a certain period of time at a certain discount rate (yield).

Interest is calculated once a year:F.V. = PV* [(1+ i) n] or FV = PV *

Interest accrual more often than once a year: FV = PV * [(1+ i / k ) nk ]

Compound interest formula - function 2

Current value of a monetary unit (P V) or current value of reversion (resale) shows what amount you need to have today in order to receive an amount equal to a monetary unit after a certain period of time at a certain discount rate (yield), that is, what amount is equivalent today to the monetary unit that we expect to receive in the future after a certain period of time.

Interest is calculated once a year: PV = FV * or PV = FV *

Interest accrual more often than once a year: PV = FV *

Compound interest formula - 3rd function

Present value of the annuity shows what amount of money today is equivalent to a series of equal payments in the future, equal to one monetary unit, for a certain number of periods at a certain discount rate.

Highlight ordinary and advance annuities. If payments are made at the end of each period, then the annuity is ordinary; if at the beginning, it is an advance annuity.

Ordinary annuity:

Interest is calculated once a year:

Interest accrual more often than once a year:

Advance annuity:

Compound interest formula - 4 function

The calculation of the real value (cost) of money is based on a temporary assessment of cash flows, which is based on the following. The purchase price of a property is ultimately determined by the amount of income that the investor expects to receive in the future. However, the purchase of real estate and the receipt of income occur at different periods of time. Therefore, a simple comparison of the magnitude of costs and income in the amount in which they will be reflected in the financial statements is impossible (for example, 10 million rubles of ready income received in 3 years will be less than this amount at present). However, the value of money is influenced not only by information processes, but also by the main condition of investment - the invested money must generate income

Bringing cash amounts that arise at different times to a comparable form is called a time estimate of cash flows. These calculations rely on compound interest, which means that the entire principal amount on deposit must earn interest, including interest remaining on the account from previous periods

The theory and practice of using compound interest functions is based on a number of assumptions: 1. Cash flow in which the amounts differ in size is called cash flow

2. A cash flow in which all amounts are equal is called an annuity

3. Cash flow amounts occur at regular intervals, called a period

4. Income received from invested capital is not withdrawn from economic turnover, but is added to the fixed capital

5. Cash flow amounts arise at the end of the period (otherwise an appropriate adjustment is required)

Let's take a closer look at the six functions of compound interest

1. Accumulated unit amount

This function allows you to determine the future value of an existing amount of money based on the expected rate of income frequency, accumulation period and interest accrual. The accumulated amount of a unit is a basic function of compound interest that allows you to determine the future value for a given period, interest rate and a known amount in the future

FV = PV * (1 + i)n Example problem: A loan of 150 million rubles was received. for a period of 2 years, at 15% per annum; % accrual occurs quarterly. Determine the accrued amount to be returned. 2. Current unit value (reversion factor)

The current value of a unit (reversion) makes it possible to determine the present (current, present) value of an amount, the value of which is known in the future for a given interest rate period. This is a process completely opposite to compound interest.

PV = FV / (1 + i)n Shows the present value of a sum of money to be received as a lump sum in the future

Example problem: What is the present value of $1,000 received at the end of the fifth year at 10% compounded annually? 3. Accumulation of a unit over a period (future value of the annuity). Shows what, at the end of the entire period, the value of a series of equal amounts deposited at the end of each periodic interval will be, i.e. the future value of the annuity. (Annuity is a cash flow in which all amounts are equal and occur at equal intervals)

FVA = (1 + i)n – 1 i PMT Example problem: Determine the future value of regular monthly payments of $12,000 for 4 years at an interest rate of 11.5% and monthly accumulation

4. Present value of an ordinary annuity. Shows the present value of a uniform stream of income, such as income generated from a rental property. The first entry occurs at the end of the first period; subsequent - at the end of each subsequent period

PVA = PMT * 1 - (1 + i)-n i Example problem: Determine the amount of the loan if it is known that $30,000 is paid annually for its repayment for 8 years at a rate of 15%. 5. Recovery Fund Factor Shows the amount of equal periodic contribution which, together with interest, is required in order to accumulate an amount equal to FVA at the end of a certain period. SFF = FVA * i (1 + i)n - 1 Example problem: Determine the amount to be deposited monthly into the bank at 15% per annum to purchase a house worth $65,000,000 in 7 years. 6. Unit Amortization Payment Shows the equal periodic payment required to fully amortize the loan, i.e. allows you to determine the amount of payment required to repay the loan, including interest and payment of principal: PMT = PVA * i 1 - (1 + i)-n Example problem: What should be the monthly payments on a self-amortizing loan of $200,000 issued on 15 years at a nominal annual rate of 12%? Topic 2. Real estate market and features of its functioning