Question

A lender providing a loan of $9 million requires semi-annual payment of interest at a nominal rate of 6.7% per year, and repayment of the $9 million principal at the end of 10 years. The borrower plans to accumulate that principal for repayment at the end of 10 years using level semi-annual deposits into a sinking fund that earns interest at a nominal rate of 3.6% per year when compounded semiannually. What is the borrower’s total cash outlay every 6?

Answer 1

The borrower’s total semi-annual outlay includes interest payments on the loan and sinking fund deposits, computed using the respective interest rates and the future value annuity formula.

The borrower’s total cash outlay every 6 months would consist of the semi-annual interest payment on the $9 million loan at a 6.7% nominal annual rate, and a semi-annual deposit into the sinking fund that earns 3.6% compounded semiannually. To calculate the semi-annual interest payment: interest per half-year = (0.067/2) * $9,000,000. To determine the sinking fund deposit: use the formula for sinking fund deposits, which involves the future value of an ordinary annuity formula. Given that the deposits are made for 10 years (20 six-month periods), the periodic deposit can be found using the formula for the future value of an ordinary annuity where FV = $9,000,000, i = 3.6%/2 per period, and n = 20 periods.

The total semi-annual outlay is the sum of the semi-annual interest payment and the semi-annual sinking fund deposit.