Question

What is the effective annual rate of 18.99 percent compounded daily?

A. less than 18.99 percent
B. 18.99 percent
C. 20.73 percent
D. 20.91 percent
E. None of the above

Answer 1

The effective annual rate (EAR) of 18.99 percent compounded daily is approximately 20.73%, calculated using the formula (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1.

Step-by-step explanation:

To calculate the effective annual rate (EAR) of 18.99 percent compounded daily, use the formula for EAR considering daily compounding. The general formula for EAR is (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1. In this case, the nominal rate is 18.99% or 0.1899, and the number of compounding periods is 365, as there are 365 days in a year.

Using the formula, the EAR is calculated as:

EAR = (1 + (0.1899 / 365))365 - 1

EAR = (1 + 0.00052)365 - 1

EAR ≈ 1.2073 - 1

EAR ≈ 0.2073 or 20.73%

So, the effective annual rate for 18.99 percent interest compounded daily is approximately 20.73 percent.