Question
Your credit card company charges you 1.36 percent per month. What is the EAR on your credit card?
Multiple Choice
18.48%
16.32%
15.50%
16.96%
17.60%
Multiple Choice
18.48%
16.32%
15.50%
16.96%
17.60%
Answers
GPT-4o mini
To calculate the Effective Annual Rate (EAR) based on a monthly interest rate of 1.36%, we can use the following formula:
\[
\text{EAR} = (1 + r)^n - 1
\]
where:
- \( r \) is the monthly interest rate (expressed as a decimal), and
- \( n \) is the number of compounding periods in one year (12 for monthly compounding).
First, convert the monthly rate from a percentage to a decimal:
\[
r = \frac{1.36}{100} = 0.0136
\]
Now, apply the values to the formula:
\[
\text{EAR} = (1 + 0.0136)^{12} - 1
\]
Calculating \( (1 + 0.0136)^{12} \):
\[
(1.0136)^{12} \approx 1.171659
\]
Subtracting 1 to find the EAR:
\[
\text{EAR} \approx 1.171659 - 1 = 0.171659
\]
Converting back to a percentage:
\[
\text{EAR} \approx 17.17\%
\]
Given the options provided, the closest correct answer is **17.60%**, though it does not match perfectly with the calculated approximation.
**Answer: 17.60%**
\[
\text{EAR} = (1 + r)^n - 1
\]
where:
- \( r \) is the monthly interest rate (expressed as a decimal), and
- \( n \) is the number of compounding periods in one year (12 for monthly compounding).
First, convert the monthly rate from a percentage to a decimal:
\[
r = \frac{1.36}{100} = 0.0136
\]
Now, apply the values to the formula:
\[
\text{EAR} = (1 + 0.0136)^{12} - 1
\]
Calculating \( (1 + 0.0136)^{12} \):
\[
(1.0136)^{12} \approx 1.171659
\]
Subtracting 1 to find the EAR:
\[
\text{EAR} \approx 1.171659 - 1 = 0.171659
\]
Converting back to a percentage:
\[
\text{EAR} \approx 17.17\%
\]
Given the options provided, the closest correct answer is **17.60%**, though it does not match perfectly with the calculated approximation.
**Answer: 17.60%**