Question

Your company has a $1,000,000. loan for a new assembly station. The interest rate for this loan is 7% compounded annually. Your company will make $100,000 payment at the end of each year, starting the end of the first year. By calculation, your company will make 18 annual payments. Payments for Year-1 through Year-17 are the same at $100,000. Payment for the last Year-18 will be less than $100,000. To payback this loan of 1M based on this payment plan, how much is the last payment for Year 18?

72,659.61

80,037.86

24,931.59

73,110.63

91,563.48

Answer 1

We have the following information

Loan = $1,000,000

Annual payment = $100,000 first 17 years

Life (n) = 18 years

Interest rate (i) = 7% or 0.07 per year

Amount paid in the 18th year = X

We will be using net present value (NPV) method

NPV = – Loan + Annual Payment(P/A, 7%, 17) + X(P/F, 7%, 18)

Equating NPV to 0

0 = – 1,000,000 + 100,000[((1+0.07)¹⁷ – 1)/0.07 (1+0.07)¹⁷] + X/(1 + 0.07)¹⁸

0 = – 1,000,000 + 976,322.30 + 0.296X

0 = – 23,677.70 + 0.2959X

23,677.70 = 0.2959X

X = 80,037.86