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 how much Phillip needs to deposit, we need to calculate the present value of an annuity. The formula for the present value of an annuity compounded annually is:

\[ PV = P \times \frac{1 - (1 + r)^{-n}}{r} \]

where:
- $ PV $ is the present value,
- $ P $ is the annual payment,
- $ r $ is the annual interest rate,
- $ n $ is the number of periods.

In this case:
- $ P = 11,500 $ (the annual payment),
- $ r = 3.50\% = 0.035 $,
- $ n = 4 $ years.

Plugging these values into the formula, we get:

\[ PV = 11,500 \times \frac{1 - (1 + 0.035)^{-4}}{0.035} \]

First, calculate $(1 + 0.035)^{-4}$:

\[ (1 + 0.035)^{-4} = 1.035^{-4} \approx 0.8790 \]

Now, plug this back into the formula:

\[ PV = 11,500 \times \frac{1 - 0.8790}{0.035} \]

\[ PV = 11,500 \times \frac{0.1210}{0.035} \]

\[ PV = 11,500 \times 3.4571 \]

\[ PV \approx 39,756.65 \]

Therefore, Phillip needs to deposit approximately $39,756.65.

Would you like further details or have any questions? Here are five related questions you might find useful:

1. How would the calculation change if the interest rate were compounded semi-annually?
2. What if Phillip needed to provide the money at the beginning of each year instead of the end?
3. How would inflation affect the real value of these payments over time?
4. What is the difference between nominal and effective interest rates?
5. How can Phillip calculate the future value of his investment if he makes monthly deposits instead?

**Tip:** When working with financial formulas, it's essential to ensure all units (time periods, interest rates) are consistent to avoid errors in calculations.

Learn how to calculate the amount needed to deposit in an investment fund growing at 3.50% annual interest to provide annual payments of $11,500 for 4 years. Detailed step-by-step solution using the present value of annuity formula. Round to the nearest cent.

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