Question

a credit card had an APR of 15.21% all of last year and compounded interest daily. what was the credit card's effective interest rate last year?

11.64%
15.21%
16.42%
16.32%

Answer 1

To find the effective interest rate (also known as the annual percentage yield, or APY) for a credit card with a given APR that compounds interest daily, we can use the following formula:

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

Where:
- \( r \) is the nominal interest rate (APR) expressed as a decimal,
- \( n \) is the number of compounding periods per year,
- \( t \) is the number of years.

In this case:
- The APR \( r = 15.21\% = 0.1521 \)
- \( n = 365 \) (daily compounding)
- \( t = 1 \) (for one year)

Now plug in the values:

\[
\text{Effective Interest Rate} = \left(1 + \frac{0.1521}{365}\right)^{365 \times 1} - 1
\]

Calculating this step-by-step:

1. Calculate \( \frac{0.1521}{365} \):

\[
\frac{0.1521}{365} \approx 0.000416
\]

2. Add 1:

\[
1 + 0.000416 \approx 1.000416
\]

3. Raise to the power of 365:

\[
(1.000416)^{365} \approx 1.1616
\]

4. Subtract 1:

\[
1.1616 - 1 \approx 0.1616
\]

5. Convert to percentage:

\[
0.1616 \times 100 \approx 16.16\%
\]

So, the effective interest rate for the credit card last year was approximately \( 16.16\% \).

Comparing this with the options you provided, it seems that none of the options match exactly. However, it is closer to \( 16.32\% \).

Therefore, the best answer choice among the options given is:
**16.32%**.