Suppose a future value annuity account of $250,000 was acquired by making quarterly payments of $2,708.63 at 5.55% compounded quarterly for 15 years. How much interest was earned?

To determine how much interest was earned on the annuity, we need to calculate the total amount of payments made over the 15 years and then subtract that from the future value of the annuity.

### Step 1: Calculate the total number of payments.
The annuity was funded by making quarterly payments for 15 years.

\[
\text{Number of payments} = 4 \times 15 = 60 \text{ payments}
\]

### Step 2: Calculate the total contributions (principal).
Each payment was $2,708.63, and there were 60 payments in total. The total amount contributed (principal) is:

\[
\text{Total contributions} = 2,708.63 \times 60 = 162,517.8
\]

### Step 3: Calculate the interest earned.
The future value of the annuity account is $250,000, and the total contributions were $162,517.80. The interest earned is the difference between the future value and the total contributions:

\[
\text{Interest earned} = 250,000 - 162,517.80 = 87,482.2
\]

### Final Answer:
The total interest earned on the annuity account is **$87,482.20**.

Would you like further clarification on any step or more details about the calculation?

Here are five related questions to extend your understanding:
1. How would the interest change if the interest rate were compounded monthly instead of quarterly?
2. What would be the total interest earned if the annuity account had a future value of $300,000?
3. How does the future value formula for annuities differ from the present value formula?
4. How would changing the payment frequency affect the total interest earned?
5. Can you calculate the effective annual rate (EAR) for the 5.55% compounded quarterly?

**Tip:** The more frequent the compounding periods, the higher the interest earned over time. This effect is called compounding frequency.

Learn how to calculate the interest earned on an annuity with a future value of $250,000, compounded quarterly at 5.55% for 15 years. Understand key concepts like future value and compound interest. Suitable for Grades 10-12.

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