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.


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Answer: B.

Reason: Compute monthly payments with formula M = P * r / (1 − (1+r)^−n).

- Bank F: r = 0.057/12 = 0.00475, n = 96. Monthly ≈ $210.67. Total paid ≈ $210.67 × 96 ≈ $20,224.
- Bank G: r = 0.062/12 ≈ 0.0051667, n = 84. Monthly ≈ $238.33. Total paid ≈ $238.33 × 84 ≈ $20,020.

So Bank F gives the lower monthly payment, but Bank G gives the lower lifetime cost. Therefore Yvette should pick F if she wants lower monthly payments, and pick G if she wants the lowest total cost.