Question

The problem describes a debt to be amortized. (Round your answers to the nearest cent.) A man buys a house for $300,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 8 years. The interest rate on the debt is 8%, compounded semiannually. (a) Find the size of each payment. (b) Find the total amount paid for the purchase. (c) Find the total interest paid over the life of the loan.

Answer 1

(a).The formula used to calculate the fixed periodic payment (P) required to fully amortize a loan of L dollars over a term of n periods at an interest rate of r per period is P = L[r (1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Here, L=150000,n=8*2=16 and r=8/200=0.04.Then,P=(150000*0.04)*(1.04)¹⁶/[(1.04)¹⁶-1] = 6000*1.872981246/0.872981246 = $ 12873.00 ( on rounding off to the nearest cent).Thus, the size of each payment is $ 12873.00.

(b). The total amount paid for the purchase is $ 150000 + 16*$ 12873 = $ 355968.

(c ). The total interest paid over the life of the loan is $ 355968 -$ 300000 = $ 55968.