What is the effective interest rate if the annual rate is 13.50% and payments are made 365 times per year?

To determine the effective interest rate when payments are made frequently, such as 365 times per year, you use the formula for the effective annual rate (EAR), which takes into account the impact of compounding. The formula for the effective interest rate is given by:

[ EAR = \left(1 + \frac{r}{n}\right)^{n} - 1 ]

where ( r ) is the nominal annual interest rate expressed as a decimal, and ( n ) is the number of compounding periods per year.

In this case, the nominal annual interest rate is 13.50%, or 0.135 as a decimal, and payments are made 365 times a year. Plugging these values into the formula:

[ EAR = \left(1 + \frac{0.135}{365}\right)^{365} - 1 ]

Performing the calculation, you first divide 0.135 by 365, then add 1 to that result, raise it to the power of 365, and finally subtract 1 to find the EAR. After going through this calculation, the resulting effective interest rate is approximately 14.45%, confirming that this calculation accounts for the