The Cooper Foundation contributes $45,000 per year into an annuity fund for building a new zoo. The fund earns 6.5% interest. Find the amount in the fund at the end of 15 years. (Round your final answer to two decimal places.)

To solve this problem, we need to determine the future value of an annuity. The Cooper Foundation contributes a fixed amount of $45,000 per year into an annuity fund, and the fund earns an interest rate of 6.5% per year. We are asked to find the amount in the fund at the end of 15 years.

The future value $ FV $ of an ordinary annuity (where payments are made at the end of each period) can be calculated using the formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

where:
- $ P $ is the annual payment,
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the total number of payments.

Given values:
- $ P = 45,000 $ dollars,
- $ r = 6.5\% = 0.065 $,
- $ n = 15 $ years.

Let's plug these values into the formula:

\[
FV = 45000 \times \frac{(1 + 0.065)^{15} - 1}{0.065}
\]

Now, let's calculate the future value step-by-step:

1. Calculate $ (1 + 0.065)^{15} $:

\[
(1 + 0.065)^{15} = 1.065^{15}
\]

2. Compute $ 1.065^{15} - 1 $:

\[
1.065^{15} \approx 2.629927195
\]

\[
1.065^{15} - 1 \approx 2.629927195 - 1 = 1.629927195
\]

3. Divide by the interest rate $ r $:

\[
\frac{1.629927195}{0.065} \approx 25.07503377
\]

4. Multiply by the annual payment $ P $:

\[
FV = 45000 \times 25.07503377 \approx 1128376.52
\]

Thus, the amount in the fund at the end of 15 years is **$1,128,376.52**.

### Would you like further details or have any questions?

### Related Questions:
1. What would the amount be if the interest rate were 5% instead of 6.5%?
2. How much interest is earned in total over the 15 years?
3. If the annual contribution was increased to $50,000, how would that affect the future value?
4. How would the future value change if contributions were made at the beginning of each year?
5. What is the present value of this annuity if the current interest rate is 6.5%?

### Tip:
When calculating the future value of an annuity, ensure that the interest rate and payment frequency match (e.g., both are annual).

Learn how to calculate the future value of an annuity with a $45,000 annual contribution, earning 6.5% interest over 15 years. Get step-by-step guidance and formulas for solving annuity problems.

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