Question

Big Brothers, Inc. borrows $242,894 from the bank at 15.15 percent per year, compounded annually, to purchase new machinery. This loan is to be repaid in equal annual installments at the end of each year over the next 9 years. How much will each annual payment be?

Answer #1

Here, the payments will be same every year, so it is an annuity. For calculating the annual payments, we will use the present value of annuity formula as below:

**PVA = P * (1 - (1 + r) ^{-n} / r)**

where, PVA = Present value of annuity = $242894, P is the periodical amount, r is the rate of interest = 15.15% and n is the time period = 9

Now, putting these values in the above formula, we get,

$242894 = P* (1 - (1 + 15.15%)^{-9} / 15.15%)

$242894 = P * (1 - ( 1+ 0.1515)^{-9} / 0.1515)

$242894 = P * (1 - ( 1.1515)^{-9} / 0.1515)

$242894 = P * (1 - 0.28094707783) / 0.1515)

$242894 = P * (0.71905292216 / 0.1515)

$242894 = P * 4.74622390871

P = $242894 / 4.74622390871

P = $51176.26

**So, annual payment is $51176.26.**

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