A bank account pays 1.33% interest every two months. What is the effective annual interest rate?

To calculate the effective annual interest rate (EAR) from an interest rate given over a different period, we use the following formula:

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

where:
- \( r \) is the interest rate for the given period,
- \( n \) is the number of periods in a year.

Given:
- The interest rate \( r = 1.33\% \) every two months,
- There are 6 periods in a year (since a year has 12 months).

Let's calculate the EAR:

\[
\text{EAR} = \left(1 + \frac{1.33\%}{1}\right)^6 - 1
\]

First, convert the percentage to a decimal:

\[
\text{EAR} = \left(1 + \frac{0.0133}{1}\right)^6 - 1
\]

Now calculate it:

\[
\text{EAR} = (1.0133)^6 - 1
\]

\[
\text{EAR} \approx 1.0827 - 1 = 0.0827
\]

\[
\text{EAR} \approx 0.0827 \times 100 = 8.27\%
\]

So, the effective annual interest rate is **8.27%**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the nominal interest rate from the effective annual rate?
2. What is the difference between nominal and effective interest rates?
3. How does compounding frequency affect the effective annual rate?
4. What would the effective annual interest rate be if the interest were compounded monthly?
5. How does the effective annual rate change if the interest rate were 2% every three months?

**Tip:** When calculating the effective annual rate, always ensure the compounding period aligns with the frequency of the interest rate provided.

Learn how to calculate the effective annual interest rate from an interest rate of 1.33% every two months. Understand the formula and steps involved, with a detailed example and calculation. Suitable for undergraduate students and anyone interested in financial mathematics.

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