To calculate the effective annual rate (EAR) when the interest is compounded quarterly, you can use the formula:
\[ \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 \]
where:
- \( r \) is the nominal interest rate (as a decimal),
- \( n \) is the number of compounding periods per year.
In this case:
- \( r = 6.00% = 0.06 \)
- \( n = 4 \) (since the interest is compounded quarterly)
Now, plug the values into the formula:
\[ \text{EAR} = \left(1 + \frac{0.06}{4}\right)^4 - 1 \]
Calculating \( \frac{0.06}{4} \):
\[ \frac{0.06}{4} = 0.015 \]
Now substitute back into the formula:
\[ \text{EAR} = \left(1 + 0.015\right)^4 - 1 \]
\[ = (1.015)^4 - 1 \]
Now calculate \( (1.015)^4 \):
\[ (1.015)^4 \approx 1.061364 \]
So,
\[ \text{EAR} \approx 1.061364 - 1 \]
\[ \text{EAR} \approx 0.061364 \]
To express this as a percentage, multiply by 100:
\[ \text{EAR} \approx 6.1364% \]
Therefore, the effective annual rate (EAR) is approximately 6.14%.