Question

A company borrows $160000, which will be paid back to the lender in one payment at the end of 5 years. The company agrees to pay semi-annually interest payments at the nominal annual rate of 10% compounded semi-annually. At the same time the company sets up a sinking fund in order to repay the loan at the end of 5 years. The sinking fund pays interest at an annual nominal interest rate of 4% compounded semi-annually. Find the total amount of the semi-annually payments, that is, the sum of the interest payment and the sinking fund payment.

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

BC $160,000.00 Loan Amount Term in years Term in years Annual interest rate Semiannual interest rate Semiannual interest payment 10% 5% $8,000.00 Sinking Fund: Semiannual interest rate No. of semiannual payment in 5 years Amount required in 5 years Semianual payment 2% 101 $160,000.00 $14,612.24 Total semi-annually payments $22,612.24 15

Cell reference -

B 160000 Loan Amount Term in years Annual interest rate Semiannual interest rate Semiannual interest payment 0.1 =C4/2 =C2*C5 Sinking Fund: Semiannual interest rate No. of semiannual payment in 5 years Amount required in 5 years Semianual payment =4%/2 =5*2 =C2 =PMT(09, C10,,-C11,0) Total semi-annually payments =C12+C6

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.