A woman buys an apartment house for $1,250,000 by making a down payment of $275,000 and amortizing the rest of the debt with semiannual payments over the next 8 years. The annual interest rate on the debt is 9.0%, compounded semiannually. Find the total amount paid over the life of the loan (excluding the down payment). Round your answer to the nearest cent.

Question

A woman buys an apartment house for $1,250,000 by making a down payment of $275,000 and amortizing the rest of the debt with semiannual payments over the next 8 years. The annual interest rate on the debt is 9.0%, compounded semiannually. Find the total amount paid over the life of the loan (excluding the down payment). Round your answer to the nearest cent. ​

Quizplus · Accepted Answer

The total amount paid over the life of the loan can be calculated using the formula for the future value of an annuity. Since the payments are semiannual, the interest rate per period is 4.5% (half of 9%), and there are 16 periods (8 years times 2). The principal amount financed is $1,250,000 - $275,000 = $975,000. Using the formula for the future value of an annuity or a loan amortization calculator, we find the semiannual payment amount and then multiply by the number of payments (16) to get the total amount paid over the life of the loan. The correct answer, after calculations, is closest to option D, $1,388,639.76. This includes both the principal and the interest paid over the 8 years.

A Woman Buys an Apartment House for $1,250,000 by Making