Question

Arnold wants to borrow $730000 for 7 years. Bank A will lend the money at j₁ = 10%, if it is amortized by monthly payments. Bank B will lend the money at j₁ = 7% if only the interest is paid monthly and the principal is paid in a lump sum at the end of 7 years. If Arnold chooses bank B he will develop a sinking fund making monthly payments earning j₄ = 3%. How much will Arnold save per payment by choosing the better option?

Answer 1

Bank A:

Monthly payment =PMT(rate,nper,pv) in excel =PMT(0.10/12,7*12,730000) = 12,118.86

Total payment = 12,118.86*7*12 =1,017,984.60

Bank B

Only Interest is paid monthly. Monthly Interest = 730,000 *0.07/12 = 4,258.33

Total interest payment over 7 years = 4,258*7*12 = 357,700

For the principal payments, he makes an investment into sinking fund.

So amount of investment =PMT(rate,nper,pv,fv) =PMT(0.03/12,7*12,0,730000) = 7820.71

Total investment for 7 years = 7820.71*12*7 = 656,939.56

Total payment = 357,700 + 656,939.56 = 1,014,639.56

Savings = 1,017,984.60 - 1,014,639.56 = $ 3,344.44