The formula for the effective annual rate (EAR) is:
EAR = \left(1 + \frac{r}{n}\right)^n - 1
Where:
- \( r \) = nominal annual interest rate (0.06 for 6%)
- \( n \) = number of compounding periods per year (4 for quarterly)
Step 1: Substitute the given values into the formula.
EAR = \left(1 + \frac{0.06}{4}\right)^4 - 1
Step 2: Calculate \(\frac{0.06}{4}\):
\frac{0.06}{4} = 0.015
Step 3: Add 1 to the result of Step 2:
1 + 0.015 = 1.015
Step 4: Raise the result of Step 3 to the power of 4:
(1.015)^4
Step 5: Calculate the power:
(1.015)^4 \approx 1.06136
Step 6: Subtract 1 from the result of Step 5 to find EAR:
1.06136 - 1 = 0.06136
Step 7: Convert the result to a percentage:
0.06136 \times 100 \approx 6.14\%
Therefore, the effective rate is:
6.14\%