Question

2), How large must each payment be if the loan is for $50,000, the interest rate is 10%, and the loan is paid off in equal installments at the end of each of the next 10 years? The loan is for the same amount as the loan in part 1, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part 1?   Please calculate the total interest payment for the 10 years loan.

Answer 1

Calculating Annual Payment over 10 years,

Using TVM Calculation,

PMT = [FV = 0, PV = 50,000, N = 10, I = 0.10]

PMT = $8,137.27

Calculating Semi-Annual Payment over 10 years,

Using TVM Calculation,

PMT = [FV = 0, PV = 50,000, N = 20, I = 0.10/2]

PMT = $4,012.13

Extra Interest = 10(8,137.27) - 20(4,012.13)

Extra Interest = $1,130.10

As payment is semi-annual interest will be applied less as half of the amount will be paid every 6 months so comppoundind of interest reduces