Question

Your credit card company charges you 1.35 percent per month. What is the annual percentage rate on your account?

a) 16.55%
b) 16.39%
c) 16.20%
d) 16.45%
e) 16.30%

Answer 1

The annual percentage rate on your account, with a monthly interest rate of 1.35 percent, is b) 16.39%.

Step-by-step explanation:

To determine the annual percentage rate (APR) from a monthly rate, we use the formula for compound interest, which calculates the total growth of an investment or debt over time. The formula for converting a monthly rate to an annual rate is
`\(APR = (1 + \text{monthly rate})^(12) - 1\)`. In this case, the monthly rate is 1.35 percent.

To calculate:

First, convert the monthly rate to a decimal: 1.35 percent = 0.0135.

Next, apply the formula:
`\(APR = (1 + 0.0135)^(12) - 1\)`.

Calculate the value inside the parentheses:
`\(1 + 0.0135 = 1.0135\)`.

Raise this value to the power of 12:
`\(1.0135^(12) \approx 1.1639\)`.

Subtract 1 from this result:
`\(1.1639 - 1 = 0.1639\)`.

Finally, convert this decimal to a percentage:
`\(0.1639 * 100 = 16.39%\)`. Therefore, the annual percentage rate (APR) on your credit card account, given a monthly interest rate of 1.35 percent, is approximately 16.39% (option b). This represents the total interest accrued over a year on your credit card balance.