Question

5. A person has applied for a loan of $ 25,000 to a banking institution that charges an interest rate of 12% per year, compounded semi-annually. If she wants to repay the loan in eight equal annuities, but make the first payment on credit until the end of the third year, and thereafter pay it annually, determine the size (amount) of these annuities (8).

Answer 1

A person has applied for a loan of $ 25,000 to a banking institution that charges an interest rate of 12% per year, compounded semi-annually.

Interest rate = 12% compounded semiannually,

So, effective annual rate = (1+APR/n)^n - 1 = (1 + 0.12/2)^2 - 1 = 12.36%

If she wants to repay the loan in eight equal annuities, but make the first payment on credit until the end of the third year

So, calculated loan amount at end of year 2 using compounding formula

Loan amount at end of year 2 = loan*(1+r)^2 = 25000*1.1236^2 = $31561.92

thereafter pay it annually. So annual payment is calculated using ordinary annuity formula

PMT = PV*r/(1 - (1+r)^-t) = 31561.92*0.1236/(1 - 1.1236^-8) = $6433.63

So, size of annuities = $6433.63