Question

Maria is going to take out a loan with a principal of $19,700. She has narrowed down her options to two banks. Bank M charges an interest rate of 7.1%, compounded monthly, and requires that the loan be paid off in five years. Bank N charges an interest rate of 7.8%, compounded monthly, and requires that the loan be paid off in four years. How would you recommend that Maria choose her loan?
a.
Bank M offers a better loan in every regard, so Maria should choose it over Bank N’s.
b.
Maria should choose Bank M’s loan if she cares more about lower monthly payments, and she should choose Bank N’s loan if she cares more about the lowest lifetime cost.
c.
Maria should choose Bank N’s loan if she cares more about lower monthly payments, and she should choose Bank M’s loan if she cares more about the lowest lifetime cost.
d.
Bank N offers a better loan in every regard, so Maria should choose it over Bank M’s.

Answer 1

Compute each loan’s monthly payment and total cost.

Bank M: r = 0.071/12 = 0.0059166667, n = 60.
Monthly payment = 19700 * r / (1 - (1+r)^(-60)) ≈ $391.44.
Total paid ≈ $391.44 × 60 = $23,486.64.

Bank N: r = 0.078/12 = 0.0065, n = 48.
Monthly payment = 19700 * r / (1 - (1+r)^(-48)) ≈ $478.26.
Total paid ≈ $478.26 × 48 = $22,956.27.

So Bank M gives the lower monthly payment, while Bank N gives the lower lifetime cost. That matches choice b.