Question

Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?

Answer 1

We should use the formula of effective annual rate:

$$r = (1 + i/n)^n - 1$$

$r$ is the effective annual rate, $i$ the nominal rate, and $n$ the number of compounding periods per year

In the first case $r = (1+0.065/12)^12 - 1 = 0.06697 = 6.7\%$

In the second case $r = (1+0.07/1)^1 - 1 = 0.07 = 7\%$

So, the effective annual rate charged by Midwest is $0.3\%$ higher versus the rate charged by Riverside.