When Aroon was a small​ child, his grandfather established a trust fund for him to receive ​$18 comma 000 on his 35th birthday. Aroon just turned 23. What is the value of his trust today if the trust fund earns 9 percent​ interest? If he had to wait until age 40 to receive the​ money, what is the present value today of the ​$18 comma 000 to be received in 17 ​years?

### Part 1: Present Value of the Trust Today at Age 35

The formula for calculating the present value (PV) of an amount to be received in the future, considering interest, is:

\[
PV = \frac{FV}{(1 + r)^n}
\]

Where:
- $ PV $ = Present value
- $ FV $ = Future value = \$18,000
- $ r $ = Interest rate per period = 9% = 0.09
- $ n $ = Number of periods = 35 - 23 = 12 years

Let's calculate the present value for receiving the money at age 35.

\[
PV = \frac{18,000}{(1 + 0.09)^{12}}
\]

### Part 2: Present Value of the Trust Today at Age 40

In this case, Aroon would receive the money at age 40, meaning the number of periods is 40 - 23 = 17 years. We can use the same formula with $ n = 17 $.

\[
PV = \frac{18,000}{(1 + 0.09)^{17}}
\]

Let me calculate both values.### Results:

- The present value of Aroon's trust today if he receives \$18,000 on his 35th birthday (12 years from now) is approximately **\$6,399.63**.
- If he had to wait until age 40 (17 years from now) to receive the \$18,000, the present value today would be approximately **\$4,159.32**.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. How would the present value change if the interest rate were 7% instead of 9%?
2. What would be the future value if the trust were compounded monthly at 9% for 12 years?
3. How does the length of time affect the present value for a given interest rate?
4. Can the present value be greater than the future value? Why or why not?
5. What is the difference between simple interest and compound interest in present value calculations?

**Tip:** The longer the time horizon or the higher the interest rate, the smaller the present value of a future amount.

When Aroon was a small​ child, his grandfather established a trust fund for him to receive ​$18,000 on his 35th birthday. Aroon just turned 23. What is the value of his trust today if the trust fund earns 9 percent​ interest? If he had to wait until age 40 to receive the​ money, what is the present value today of the ​$18,000 to be received in 17 ​years?

Calculate the present value of a trust fund set to deliver $18,000 on Aroon's 35th birthday, with 9% annual interest. Learn how to use the present value formula and understand the time value of money over 12 and 17 years. Perfect for finance students and advanced high school learners.

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