When Aroon was a small​ child, his grandfather established a trust fund for him to receive ​$20000 on his 35th birthday. Aroon just turned 23. What is the value of his trust today if the trust fund earns 7 percent​ interest? If he had to wait until age 40 to receive the​ money, what is the present value today of the ​$20000 to be received in 17 ​years?
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Part 1
Click the following table icon to view the PVIF​ table: LOADING....
The present​ value, PV​, of his trust today if the trust fund earns 7 percent interest is ​$

enter your response here.  ​(Round to the nearest​ cent.)
Part 2
The present​ value, PV​, if he had to wait until age 40 to receive the money is ​$

enter your response here.  ​(Round to the nearest​ cent.)

To calculate the present value of Aroon's trust fund, we'll use the formula for Present Value (PV) based on compound interest:

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

Where:
- $PV$ = Present Value
- $FV$ = Future Value (the amount Aroon will receive at maturity, $20,000)
- $r$ = interest rate (7% or 0.07 annually)
- $n$ = number of years until Aroon receives the money

### Part 1: Present Value Today if Aroon Receives the Money at Age 35
Aroon just turned 23, so he will receive the $20,000 in 12 years (at age 35).

\[
PV = \frac{20,000}{(1 + 0.07)^{12}}
\]

Now, let's calculate the present value for this.

### Part 2: Present Value Today if Aroon Receives the Money at Age 40
If Aroon had to wait until age 40 to receive the money, that would be 17 years from now.

\[
PV = \frac{20,000}{(1 + 0.07)^{17}}
\]

Let's now calculate both present values.### Results:

- **Present Value today if Aroon receives the money at age 35** (in 12 years): \$8,880.24
- **Present Value today if Aroon receives the money at age 40** (in 17 years): \$6,331.49

Let me know if you'd like further details or have questions!

Here are 5 related questions for further practice:
1. What would the present value be if the interest rate were 5% instead of 7%?
2. How would the present value change if Aroon were 30 years old and still receiving the money at 35?
3. What happens to the present value if the future value is increased to $25,000?
4. How is the present value affected if the money is received in 10 years instead of 12 years?
5. Can you calculate the future value if Aroon's trust was worth \$8,000 today and earns 7% interest for 12 years?

**Tip:** The further away a future payment is, the lower its present value will be, especially with higher interest rates.

When Aroon was a small​ child, his grandfather established a trust fund for him to receive ​$20000 on his 35th birthday. Aroon just turned 23. What is the value of his trust today if the trust fund earns 7 percent​ interest? If he had to wait until age 40 to receive the​ money, what is the present value today of the ​$20000 to be received in 17 ​years?

Calculate the present value of a $20,000 trust fund Aroon will receive at age 35, using a 7% interest rate. Also, learn how to find the present value if he waits until age 40. Includes key financial concepts like compound interest and time value of money. Suitable for Grades 10-12.

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