A young man is the beneficiary of a trust fund established for him 21 years ago at his birth. If the original amount placed in trust was $20,000, how much will he receive if the money has earned interest at the rate of 9%/year compounded quarterly? (Round your final answer to two decimal places.)

To solve this problem, we need to use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

Given:
- $ P = 20,000 $ dollars,
- $ r = 9\% = 0.09 $,
- $ n = 4 $ (since the interest is compounded quarterly),
- $ t = 21 $ years.

Now, we can plug these values into the formula:

\[
A = 20000 \left(1 + \frac{0.09}{4}\right)^{4 \times 21}
\]

Let's calculate this step by step.

1. Calculate the quarterly interest rate:

\[
\frac{r}{n} = \frac{0.09}{4} = 0.0225
\]

2. Add 1 to the quarterly interest rate:

\[
1 + \frac{r}{n} = 1 + 0.0225 = 1.0225
\]

3. Calculate the exponent:

\[
nt = 4 \times 21 = 84
\]

4. Raise $1.0225$ to the power of 84:

\[
1.0225^{84} \approx 5.7977
\]

5. Multiply by the principal amount:

\[
A = 20000 \times 5.7977 \approx 115,954.37
\]

Thus, the young man will receive **$115,954.37**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the final amount change if the interest were compounded monthly instead of quarterly?
2. What would the final amount be if the trust fund was established 25 years ago instead of 21 years?
3. How does the compound interest formula differ from simple interest, and what impact does that have over long periods?
4. If the interest rate were increased to 10%, how much would the young man receive after 21 years?
5. What is the formula to calculate the time it would take for the amount to double with a fixed interest rate?

**Tip:** Remember, the more frequently interest is compounded, the more interest you earn over time!

Learn how to calculate the growth of a trust fund with compound interest. Given an initial amount of $20,000, an interest rate of 9% compounded quarterly, and a duration of 21 years, find out how much the beneficiary will receive. Includes a detailed step-by-step solution and final amount. Explore variations in compounding frequency and interest rate impact.

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