Use the formula for 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 8%
compounded monthly. Round your answer to the nearest cent, if necessary.

The formula for the present value $ PV $ of a future amount of money, compounded periodically, is given by:

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

Where:
- $ PV $ is the present value (the amount you need to invest now),
- $ FV $ is the future value (the desired amount after a certain time),
- $ r $ is the annual interest rate (APR) as a decimal,
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

### Given:
- $ FV = 25,000 $ (desired future amount),
- $ r = 0.08 $ (8% annual interest rate),
- $ n = 12 $ (compounded monthly),
- $ t = 10 $ (investment period in years).

Let’s calculate the present value using this information.

\[
PV = \frac{25,000}{(1 + \frac{0.08}{12})^{12 \times 10}}
\]

Now, I will compute this.The amount you need to invest now in one lump sum to have $25,000 after 10 years, with an 8% annual interest rate compounded monthly, is approximately **$11,263.09**.

Would you like more details on this calculation, or do you have any questions?

Here are five related questions you could explore:
1. How would the present value change if the interest rate was 6% instead of 8%?
2. What if the compounding was done quarterly instead of monthly?
3. How much would the future value be if you invested $15,000 today under the same conditions?
4. How would the required investment change for a 5-year period instead of 10 years?
5. What if the compounding was done continuously instead of monthly?

**Tip:** The more frequently interest is compounded, the higher the future value will be for the same initial investment.

Use the formula for 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 8% compounded monthly. Round your answer to the nearest cent, if necessary.

Calculate the present value of an investment required to reach $25,000 in 10 years, with an 8% APR compounded monthly. This problem explores the concept of time value of money, using the compound interest formula, and is suitable for high school students.

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