Question

Harris Machinery received a demand loan of $180,000. It repaid $70,000 at the end of the first year, $90,000 at the end of the second year, and the balance at the end of the third year. The interest rate charged on the loan was 5.75% compounded semi-annually during the first year, 5.50% compounded quarterly during the second year, and 4.75% compounded monthly during the third year.

a. What was the balance of the loan at the end of the first year?

Round to the nearest cent

b. What was the balance of the loan at the end of the second year?

Round to the nearest cent

c. What amount at the end of the third year will settle the loan?

Answer 1

a)

Future value = Present value*(1+(r/m))^m

r = rate of interest

n = number of compoundings

a)

loan value along with interest at the end of 1st year = 180000*(1+(5.75%/2))^2

= 190,498.78

repayment amount = 70,000

balance loan = 190,498.78 - 70,000 = $120,498.78

b)

loan value at the end of 2nd year = 120,498.78*(1+(5.50%/4))^4

= $127,264.16

repayment amount = 90,000

Loan balance = 127,264.16 - 90,000 = $37,264.16

c)

Loan value at the end of thid year = 37,264.16*(1+(4.75%/12))^12

= 39,073.26

Settlement amount = $39,073.26