Question

DeRestless, Inc. decides to buy a warehouse for $400,000. The company will put $50,000 down and finance the remaining amount using equal monthly payments over 15 years at an interest rate of 6% compounded monthly.

1. What is the payment?

2. Immediately after making the payment at the end of 10 years, DDIC decides to pay the remaining balance of the loan. How much will they owe?

Answer 1

(a)

Monthly (nominal) interest rate = 6%/12 = 0.5%

Number of months = 12 x 15 = 180

Loan amount = $400,000 - $50,000 = $50,000

Monthly payment = Loan amount / P/A(0.5%, 180) = $350,000 / 118.5035** = 2,953.50

(b)

After 10 years (= 120) months,

Number of months left = 180 - 120 = 60

Remaining balance = Number of months left x Monthly payment = $2,953.5 x 60 = $177,210

**P/A(0.5%, 180) = [1 - (1.005)^-180] / 0.005 = (1 - 0.4075) / 0.005 = 0.5925 / 0.005 = 118.5035