Question

Yvette is considering taking out a loan with a principal of $16,200 from one of two banks. Bank F charges an interest rate of 5.7%, compounded monthly, and requires that the loan be paid off in eight years. Bank G charges an interest rate of 6.2%, compounded monthly, and requires that the loan be paid off in seven years. How would you recommend that Yvette choose her loan?
a.
Bank F offers a better loan in every regard, so Yvette should choose it over Bank G’s.
b.
Yvette should choose Bank F’s loan if she cares more about lower monthly payments, and she should choose Bank G’s loan if she cares more about the lowest lifetime cost.
c.
Yvette should choose Bank G’s loan if she cares more about lower monthly payments, and she should choose Bank F’s loan if she cares more about the lowest lifetime cost.
d.
Bank G offers a better loan in every regard, so Yvette should choose it over Bank F’s.

Answer 1

Compute the monthly payment using the loan amortization formula
payment = L * i / (1 − (1+i)^−n),
where i = annual rate/12 and n = months.

Bank F: i = 0.057/12 ≈ 0.00475, n = 8·12 = 96
→ monthly ≈ $211, total paid ≈ $211·96 ≈ $20,258

Bank G: i = 0.062/12 ≈ 0.0051667, n = 7·12 = 84
→ monthly ≈ $238, total paid ≈ $238·84 ≈ $20,020

So Bank F gives the lower monthly payment, but Bank G gives the lower lifetime cost (total paid). Therefore choose Bank F if you care most about lower monthly payments and Bank G if you care most about the lowest lifetime cost. Answer: (b).