A friend wants to borrow money from you. He states that he will pay you $2,700 every 6 months for 9 years with the first payment exactly 5 years and six months from today. The interest rate is an APR of 7.3 percent with semiannual compounding. What is the value of the payments today?

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Business

Ripley

24 April, 05:06

A friend wants to borrow money from you. He states that he will pay you $2,700 every 6 months for 9 years with the first payment exactly 5 years and six months from today. The interest rate is an APR of 7.3 percent with semiannual compounding. What is the value of the payments today?

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Amara Weber · Answer 1

The value of the payment today = $36,539.65

Explanation:

An annuity is a series of equal payment or receipt occurring for certain number of period.

The payment in question is an example of an annuity. Hence the value of the payment today would be the present value of 2,700 annuity discounted at the appropriate interest rate.

This is done as follows:

The Present Value of annuity = A * (1 - (1+r) ^ (-n)) / r

A - periodic cash flow-2,700, r - semi annual rate of interest - 7.3/2 = 3.65%

n - number of period - (9*2) + 1 = 19. Note that we have 19 "six months" in 9 years 6 months

PV = 2,700 * (1 - (1+0.0365) ^ (-19)) / 0.0365 = 36,539.650

The value of the payment today = $36,539.65