Question

Arnold wants to borrow $730000 for 7 years. Bank A will lend the
money at j_{1} = 10%, if it is amortized by monthly
payments. Bank B will lend the money at j_{1} = 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 j_{4} = 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**

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