Jonathan and Agustina have a new grandson. How much money should they invest now so that he will have $79,000 for his college education in 18 years? The money is invested at 7.55% compounded quarterly

To calculate how much Jonathan and Agustina should invest now, we can use the **present value formula** for compound interest:

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

Where:
- $PV$ is the present value (the amount they should invest now),
- $FV$ is the future value (the amount they want in the future, \$79,000),
- $r$ is the annual interest rate (7.55% or 0.0755 as a decimal),
- $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$),
- $t$ is the number of years the money will be invested (18 years).

### Plugging in the values:

- $FV = 79,000$,
- $r = 0.0755$,
- $n = 4$,
- $t = 18$.

\[
PV = \frac{79,000}{\left(1 + \frac{0.0755}{4}\right)^{4 \times 18}}
\]

Let me calculate this for you.Jonathan and Agustina should invest approximately **$20,555.21** now in order to have $79,000 in 18 years for their grandson's college education, assuming an interest rate of 7.55% compounded quarterly.

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions you might consider:
1. How does changing the interest rate affect the required investment?
2. What happens if the interest is compounded monthly instead of quarterly?
3. How much would the investment be worth after 10 years instead of 18 years?
4. What if they wanted to withdraw the money over 4 years instead of as a lump sum?
5. How does inflation affect the real value of the $79,000 in 18 years?

**Tip**: Compounding frequency (quarterly, monthly, etc.) significantly impacts how much you need to invest initially.

Jonathan and Agustina have a new grandson. How much money should they invest now so that he will have $79,000 for his college education in 18 years? The money is invested at 7.55% compounded quarterly.

Learn how to calculate the present value of an investment required for a college fund of $79,000 in 18 years, assuming a 7.55% interest rate compounded quarterly. This detailed solution is suitable for high school students and those studying finance, covering compound interest concepts and the present value formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation