A young man is the beneficiary of a trust fund established for him 25 years ago at his birth. If the original amount placed in trust was $40,000, 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.)
$ 

Select the formula used to solve this problem?


A. 

*I* = *Prt*

B. 

*A* = *P*(1+*rt*)

    C. 

*A* = *P*(1+*i*)*n*, *i*=

*r*

*m*

, *n*=*mt*

D. 

*reff* = 1+

*r*

*m*

*m*
 
 − 1

E. 

*reff* = 

*A*

*P*

1/*t*
 
 − 1

To solve this problem, we use the compound interest formula, which is suitable for situations where interest is compounded multiple times per year. The correct formula for compound interest is:

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

**Given:**
- $ P = 40,000 $ (initial amount)
- $ r = 0.09 $ (annual interest rate in decimal)
- $ n = 4 $ (compounded quarterly, so 4 times a year)
- $ t = 25 $ years

Plugging the values into the formula:

\[
A = 40000 \left(1 + \frac{0.09}{4}\right)^{4 \times 25}
\]

First, calculate the term inside the parentheses:

\[
1 + \frac{0.09}{4} = 1 + 0.0225 = 1.0225
\]

Now calculate the exponent:

\[
4 \times 25 = 100
\]

Substitute these values into the formula:

\[
A = 40000 \times (1.0225)^{100}
\]

Calculating $(1.0225)^{100}$:

\[
(1.0225)^{100} \approx 9.646293
\]

Now, find $ A $:

\[
A = 40000 \times 9.646293 \approx 385851.72
\]

So, the young man will receive approximately **$385,851.72**.

**The correct formula used to solve this problem is:**

**C.** $ A = P(1 + i)^n $, where $ i = \frac{r}{m} $ and $ n = mt $.

Would you like more details or have any other questions? Here are some related questions you might find interesting:

1. What would the amount be if the interest rate was 8% compounded annually?
2. How would the amount change if it was compounded monthly instead of quarterly?
3. What if the interest was compounded continuously? How would you calculate it?
4. How long would it take for the $40,000 to double with a 9% annual rate compounded quarterly?
5. What if the initial investment was $50,000 instead of $40,000, with the same interest rate and compounding period?

**Tip:** When solving compound interest problems, remember to adjust the interest rate and number of compounding periods based on how often the interest is compounded. This ensures accurate calculations.

Learn how to calculate the growth of a trust fund using compound interest. Given an initial amount of $40,000, an interest rate of 9% compounded quarterly over 25 years results in approximately $385,851.72. Understand the compound interest formula and its application. Suitable for high school students studying financial mathematics.

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