Calculate the amount of money Phillip had to deposit in an investment fund growing 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, throughout undergraduate studies.
Round to the nearest cent

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.

Learn how to calculate the amount of money needed to deposit in an investment fund growing at 3.50% annual interest to provide $11,500 annually for 4 years. Detailed step-by-step solution using the Present Value of an Annuity formula. Suitable for advanced high school and college students.

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