Accumulation of monetary unit for the period, Amortization contribution...

Accumulation of a monetary unit for a period

Based on the use of this function, the future value of a series of equal periodic payments (receipts) is determined.

Similar to the conditions considered for the previous function, payments can be made both at the end and at the beginning of each time period.

The future value of a regular annuity for payments made once at the end of the year:

For payments made more than once a year:

The future value of the advance annuity for payments made once at the beginning of the year:

With advance payments made more often than once a year:

Contribution to unit depreciation

Depreciation in finance theory is the process of repaying a debt over a period of time. A contribution to the amortization of a monetary unit indicates how a compulsory periodic periodic payment of a loan will be made, allowing repayment of the loan within a specified period. This value is defined as the inverse of the current value of the annuity.

Each equal contribution to the depreciation of the unit includes the percentage - return on investment and the payment of part of the original principal amount of the loan - return on investment.

The ratio of these two components varies with each payment.

The contribution to the amortization of a monetary unit is defined as the ratio of one payment to the original principal amount of the loan:

This formula is used to build pre-calculated tables.

Calculation of the usual contribution to the depreciation of a monetary unit for the n-th period can be done using the formula:

Example

What are the monthly payments for a self-amortizing loan of 200,000 rubles, granted for 25 years at a nominal annual rate of 12%?

РМТ = 200 000 х 0.015322 (column 6; п = 25; i = 12%) = = 3064.4 rub. * 1

Recovery fund factor

Reimbursement fund factor shows the amount of money that must be paid at the end of each period so that after a specified number of periods the balance is 1 den. units This is the inverse of the unit accumulation factor for the period, and takes into account only the return of the invested funds.

When calculating the factor of the reimbursement fund use the formula:

The factors obtained are placed in column 3 of the previously calculated tables.

Mathematically, the record corresponds to the formula:

Example

Within five years, it is required to save 15,000 rubles, depositing monthly equal amounts of money. The interest rate will be 11%, the interest will be charged every month. Determine the amount of the monthly deposit.

PMT = 15,000 x 0.0125758 (column factor 3; i = 11%; n = 5) = 188, 64 rubles.

If the deposit of money is made at the beginning of the period, then the formula of the advance recovery fund factor should be used.

In real estate valuation, this function is used:

• to accumulate the amount of funds to repay the debt in the future;

• when forming the so-called reserve for the replacement of short-lived elements of the real estate object.

The considered functions of compound interest are used in investment calculations, in particular within the framework of mortgage investment analysis, which is a variant of the income approach with the availability of borrowed capital.

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