Which of the following loan terms would result in the lowest annual cost?
A)4% compounded annually
B)4%, compounded monthly
C)4%, compounded quarterly
D)4%, compounded daily

Question

Quizplus · Accepted Answer

The loan term with the lowest annual cost is the one with the lowest effective annual interest rate (APY). The effective annual interest rate is calculated as (1 + (nominal rate/number of times compounded per year))^number of times compounded per year - 1. Therefore, for a 4% nominal rate, the effective annual interest rate would be:

A) (1 + (4%/1))^1 - 1 = 4.00%
B) (1 + (4%/12))^12 - 1 = 4.07%
C) (1 + (4%/4))^4 - 1 = 4.08%
D) (1 + (4%/365))^365 - 1 = 4.09%

As we can see, option A has the lowest effective annual interest rate and therefore results in the lowest annual cost. The loan with the lower compounding frequency will result in a lower annual cost. Since option A is compounded annually, it will have the lowest annual cost.

Which of the Following Loan Terms Would Result in the Lowest