Question

The First Bank of Lending lists the following APR for loans. Determine the APY, or effective interest rate, for a loan amount that is less than $20,000

. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.

Answer 1

The effective interest rate, or APY, for loans under $20,000 with a 14.25% APR compounded daily is approximately 15%.

To determine the APY, or effective interest rate, for a loan amount that is less than $20,000, we need to use the following formula:

APY = (1 + (APR/n))^n - 1

where APR is the annual percentage rate, and n is the number of compounding periods per year.

According to the table in the image, the APR for loan amounts less than $20,000 is 14.25%, and the interest rates are compounded daily. Therefore, we can plug in these values into the formula:

APY = (1 + 0.1425/365)^365 - 1

Using a calculator, we can simplify this expression and get:

APY ≈ 0.1548

To round this answer to the nearest hundredth, we look at the third decimal place and see that it is 4, which is less than 5. Therefore, we do not change the second decimal place and drop the rest of the digits. The final answer is:

APY ≈ 0.15

This means that the effective interest rate for a loan amount that is less than $20,000 is about 15%.