Question

Mr. Bronson wants to be one of the investors in the new Sergio Leone movie called The Good, The Bad and The Ugly. He needs to borrow $1580000 from a bank at an interest rate of 6.9% compounded quarterly to invest in this movie. The loan will be repaid in 27 equal monthly payments. His first payment will be made one month after the day he borrows the money (i.e. at the end of month one). (round your final answers to 4 decimal point)

1. What is the amount of his monthly payments?
2. What are the interest and principal payments in his 7^th monthly payment. (round your final answers to 1 decimal point)

Answer 1

i = 6.9% / 4 = 1.725% per quarter

Let monthly rate be r, then as per given condition

0.01725 = (1+r)^3 + 1

(1+r)^3 = 1.01725

1+r = 1.01725 ^(1/3) = 1.005717

r = 1.005717 - 1 = 0.005717

a.

Monthly payment = 1580000 * (A/P,0.5717%,27)

= 1580000 * 0.005717 * ((1 + 0.005717)^27)/((1 + 0.005717)^27-1)

= 1580000 * 0.005717 * ((1.005717)^27)/((1.005717)^27-1)

= 1580000 * 0.0400746

= 63317.8801 (Round to four decimal places)

b.

Loan principal amount remaining after 6 payment = 63317.8801 *(P/A,0.5717%,21)

= 63317.8801 *((1 + 0.005717)^21-1)/(0.005717 * (1 + 0.005717)^21)

= 63317.8801 *((1.005717)^21-1)/(0.005717 * (1.005717)^21)

= 1249599.03

Interest amount in 7th payment = 1249599.03 * 0.005717 = 7143.9576 ~ 7143.96 ~ 7144.0 (round to one decimal places)

Principal amount of 7th payment = 63317.88 - 7143.96 = 56173.92 ~ 56174.0 (round to one decimal places)