Question

A savings loan offers 6% compounded quarterly. What is the effective rate to two decimal places? O 6.40% O 6.23% O 6.14% 0 6.27%

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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\%

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.

Step 2: Calculate \(\frac{0.06}{4}\):

Step 3: Add 1 to the result of Step 2:

Step 4: Raise the result of Step 3 to the power of 4:

Step 5: Calculate the power:

Step 6: Subtract 1 from the result of Step 5 to find EAR:

Step 7: Convert the result to a percentage:

Therefore, the effective rate is:

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