Question

A store credit card charges an APR of 12% that is compounded once a month. What is the APY for the credit line?

(1 point)
Responses

12.12%

12.12%

12.34%

12.34%

12.52%

12.52%

12.68%

Answer 1

To calculate the Annual Percentage Yield (APY) from an Annual Percentage Rate (APR) that is compounded monthly, you can use the following formula:

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

Where:
- \( r \) is the annual interest rate (APR) expressed as a decimal.
- \( n \) is the number of compounding periods per year (12 for monthly).
- \( t \) is the time in years (1 year for APY).

For the given problem:
- \( r = 0.12 \)
- \( n = 12 \)
- \( t = 1 \)

Plugging in the values:

\[
\text{APY} = \left(1 + \frac{0.12}{12}\right)^{12 \times 1} - 1
\]

Calculating the fraction:

\[
\text{APY} = \left(1 + 0.01\right)^{12} - 1
\]
\[
\text{APY} = (1.01)^{12} - 1
\]

Now calculating \( (1.01)^{12} \):

\[
(1.01)^{12} \approx 1.126825
\]

Subtracting 1 to find the APY:

\[
\text{APY} \approx 1.126825 - 1 \approx 0.126825
\]

Converting it back to a percentage:

\[
\text{APY} \approx 0.126825 \times 100 \approx 12.6825\%
\]

Rounding this to two decimal places gives us:

\[
\text{APY} \approx 12.68\%
\]

Thus, the APY for the credit line is **12.68%**.