Question

1) Enter your answer in this format: 1.23 (hundredths)

A. Benji made a down payment of $28,660 on a house. The monthly loan payment for the house is $2,121 for 20 years. The nominal annual interest on the loan is 12%, compounded monthly. What was the original sale price of the house?

B. Benji has a quarterly loan payment of $4,820 for 3 years. The bank charges a nominal annual interest rate of 3% compounded quarterly for the loan. If Benji makes all of the payments as scheduled, how much total interest will Benji pay to the bank over the life of the loan?

C. Benji has a semi-annual (two times a year) loan payment of $1,003 for 14 years. The bank charges a nominal annual interest rate of 12% compounded semi-annually for the loan. How much of loan payment 23 will go towards paying the principal?

Answer 1

A. I = 12% / 12 = 1% per month

t = 20 * 12 = 240 months

Sale price of house = 28660 + 2121 * (P/A, 1%,240) = 28660 + 2121 * 90.819416 = 221287.98

B.

I = 3% / 4 = 0.75% per quarter

t = 3 yrs = 3*4 = 12 quarters

Loan amount = 4820 * (P/A, 0.75%,12) = 4820 * 11.434913 = 55116.28

Interest paid over loan period = 4820 * 12 - 55116.28 = 2723.72

C.

Total loan payment = 14 * 2 = 28

I = 12% / 2 = 6% per semiannual period

Principal unpaid after 22 payment = 1003 * (P/A, 6%,6) = 1003 * 4.917324 = 4932.08

Interest in 23rd payment = 4932.08 * 0.06 = 295.92

Principal in 23rd payment = 1003 - 295.92 = 707.08