First Bank offers XYZ Company a 1-year variable rate loan at a rate of prime plus ½%. Prime rate is 3%. Payments must be made monthly and there are no other fees. What is the effective annual cost of this loan?
A) .29%
B) 3.00%
C) 3.50%
D) 3.56%

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) for a loan with monthly payments and a nominal rate of prime plus ½% (3.5% in this case) can be calculated using the formula for EAR with monthly compounding: $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual nominal rate (0.035 for 3.5%) and $n$ is the number of compounding periods per year (12 for monthly). Plugging in the values, we get $EAR = (1 + \frac{0.035}{12})^{12} - 1$, which approximates to 3.56%.

First Bank Offers XYZ Company a 1-Year Variable Rate Loan