To determine the amount of money Phillip needed to deposit in a fund that grows at an interest rate of 3.50% compounded annually to provide his daughter with $11,500 at the end of every year for 4 years, we will use the Present Value of an Annuity formula.

Given:

• Future payment ($PMT$) = $11,500
• Number of periods ($n$) = 4 years
• Interest rate per period ($i$) = 3.50% = 0.035

Formula for Present Value of an Annuity:

$PV = PMT \left( \frac{1 - (1 + i)^{-n}}{i} \right)$

Step-by-Step Calculation:

1. Calculate the factor: $(1 + i)^{-n} = (1 + 0.035)^{-4} \approx 1.035^{-4} \approx 0.8792$

2. Subtract this from 1: $1 - 0.8792 = 0.1208$

3. Divide by the interest rate: $\frac{0.1208}{0.035} \approx 3.4514$

4. Multiply by the annual payment: $PV = 11500 \times 3.4514 \approx 39691.10$

Therefore, Phillip needs to deposit approximately $39,691.10 to provide his daughter with $11,500 at the end of every year for 4 years.

Would you like more details or have any questions?

Here are some related questions you might want to explore:

1. What would be the present value if the interest rate was 5% instead?
2. How much would Phillip need to deposit if the payments were made at the beginning of each year?
3. What is the total amount Phillip's daughter will receive over the 4 years?
4. How much interest will Phillip earn over the 4 years?
5. How would the present value change if the duration was 5 years instead of 4?

Tip: When calculating present value, ensuring the interest rate and periods align with the compounding and payment schedule is crucial for accurate results.