Question

A company borrows $170000, which will be paid back to the lender in one payment at the end of 6 years. The company agrees to pay yearly interest payments at the nominal annual rate of 13% compounded yearly. At the same time the company sets up a sinking fund in order to repay the loan at the end of 6 years. The sinking fund pays interest at an annual nominal interest rate of 5% compounded yearly. Find the total amount of the yearly payments, that is, the sum of the interest payment and the sinking fund payment.

Answer 1

Answer: sum of interest and sinking fund payment =$42979.39

Workings:

Calculation of interest payments on the borrowing:

Interest = 170000*13/100

=$22100per annum

Calculation of sinking fund payments every year for 6 years:

P= A(r/n)÷[(1+r/n)^nt-1]

P is the annual deposit amount

A is the amount at the end of 6 years = 170000

r is the rate of interest =5%

n is the compounding =1

t is the no.of years=6

P= 170000(0.05)÷[(1+0.05)^6-1]

=8500÷0.4071=20879.39

Anual sinking fund payment is $20879.39

Therefore, total anual payment of interest and sinking fund payment = 22100+20879.39=$42979.39