The Cooper Foundation contributes $20,000 per year into an annuity fund for building a new zoo. The fund earns 5.5% 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 use the future value of an annuity formula, which is given by:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the annual payment (in this case, $20,000).
- $ r $ is the annual interest rate (as a decimal, so 5.5% becomes 0.055).
- $ n $ is the number of payments (in this case, 15 years).

Let's calculate it:

\[
FV = 20000 \times \frac{(1 + 0.055)^{15} - 1}{0.055}
\]

First, calculate $ (1 + 0.055)^{15} $:

\[
(1 + 0.055)^{15} = 1.055^{15}
\]

Next, subtract 1 and divide by 0.055:

\[
\frac{(1.055)^{15} - 1}{0.055}
\]

Finally, multiply by the annual payment:

\[
FV = 20000 \times \left(\frac{(1.055)^{15} - 1}{0.055}\right)
\]

I'll calculate this step-by-step.The amount in the fund at the end of 15 years is approximately **$448,173.27**.

Do you want further details or have any questions? Here are five related questions that might interest you:

1. How would the future value change if the interest rate were 6% instead of 5.5%?
2. What would be the future value if the contributions were made monthly instead of annually?
3. How much interest is earned over the 15 years?
4. If the foundation decided to stop contributing after 10 years, what would the fund amount to at the end of 15 years?
5. How would the future value change if the annual contribution were increased to $25,000?

**Tip:** When dealing with annuities, always ensure the interest rate and payment frequency are consistent (e.g., annual payments with an annual interest rate).

Learn how to calculate the amount in an annuity fund after 15 years with annual contributions of $20,000 and a 5.5% interest rate. Explore step-by-step solutions using the future value of annuity formula. Suitable for high school students and anyone interested in finance calculations.

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