Question

A company borrows $200000, which will be paid back to the lender in one payment at the end of 8 years. The company agrees to pay monthly interest payments at the nominal annual rate of 4% compounded monthly. At the same time the company sets up a sinking fund in order to repay the loan at the end of 8 years. The sinking fund pays interest at an annual nominal interest rate of 13% compounded monthly. Find the total amount of the monthly payments, that is, the sum of the interest payment and the sinking fund payment.

Total monthly payment = $

Answer 1

Monthly interest rate of borrowing = 4 % /12 = 0.04/12 or 0.003333333

Monthly interest amount for $ 200,000 = 0.003333333 x $ 200,000 = $ 666.67

Future amount of sinking fund = $ 200,000

Monthly payment of sinking fund can be computed using future value of annuity as:

FV = P x [{(1+r) ⁿ – 1}/r]

FV = Future value of fund = $ 200,000

P = Periodic payment

r = Rate per period = 0.13/12 or 0.010833333 p.m.

n = no. of periods = 8 x 12 = 96

$ 200,000 = P x [{(1+0.010833333)⁹⁶ – 1}/0.010833333]

               = P x [{(1.010833333)⁹⁶ – 1}/0.010833333]

               = P x [(2.81343744 – 1)/0.010833333]

               = P x (1.81343744/0.010833333)

               = P x 167.3942253

P = $ 200,000/167.3942253

P = $ 1,194.78

Total monthly payments = $ 666.67 + $ 1,194.78 = $ 1,861.45