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To solve the problem in the image, we need to use the **present value formula** for compound interest. The problem is asking how much you should invest now (the present value) to have $25,000 after 10 years, with an annual percentage rate (APR) of 3% compounded quarterly.

The formula for the present value $ PV $ is:

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

Where:
- $ PV $ = Present Value (the amount you need to invest now)
- $ FV $ = Future Value (the amount you want in the future, $25,000 in this case)
- $ r $ = Annual interest rate (APR) as a decimal (3% = 0.03)
- $ n $ = Number of times the interest is compounded per year (quarterly means 4 times)
- $ t $ = Number of years the money is invested (10 years)

Let's plug in the values:
- $ FV = 25,000 $
- $ r = 0.03 $
- $ n = 4 $
- $ t = 10 $

The formula becomes:

\[
PV = \frac{25,000}{(1 + \frac{0.03}{4})^{4 \times 10}}
\]

I'll now calculate this.The amount you need to invest now in one lump sum is approximately **$18,541.20** to reach $25,000 in 10 years with an APR of 3%, compounded quarterly.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. How does the compounding frequency affect the present value?
2. What would happen to the present value if the interest rate was higher?
3. How would the present value change if the interest was compounded monthly instead of quarterly?
4. What is the future value if you invest $18,541.20 for 10 years at 3% APR compounded annually?
5. How can you adjust the formula if interest is compounded continuously?

**Tip:** The more frequently interest is compounded, the greater the future value will be due to the effect of compound interest.

Use the formula for the present value of money to calculate the amount you need to invest now in one lump sum in order to have $25,000 after 10 years with an APR of 3% compounded quarterly. Round your answer to the nearest cent, if necessary.

Learn how to calculate the present value of money with a 3% APR compounded quarterly. Find out how much you need to invest now to have $25,000 in 10 years. This problem covers key financial concepts, including compound interest and the present value formula.

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