Guyton and Jessica 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 4.1% compounded quarterly.

To solve this problem, we will use the formula for compound interest to determine the present value (the amount of money that should be invested now).

The compound interest formula is:

\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]

Where:
- $ A $ is the future value (amount after interest), which is $79,000.
- $ P $ is the present value (the amount to be invested).
- $ r $ is the annual interest rate (as a decimal), which is 4.1% or 0.041.
- $ n $ is the number of times the interest is compounded per year, which is 4 (quarterly).
- $ t $ is the number of years the money is invested, which is 18 years.

We are solving for $ P $. Rearranging the formula to solve for $ P $:

\[
P = \frac{A}{\left( 1 + \frac{r}{n} \right)^{nt}}
\]

Now we can substitute the known values:

\[
P = \frac{79,000}{\left( 1 + \frac{0.041}{4} \right)^{4 \times 18}}
\]

Let me calculate that for you.Guyton and Jessica should invest approximately **$37,909.60** now so that their grandson will have $79,000 for his college education in 18 years, given a 4.1% interest rate compounded quarterly.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to explore further:
1. How would the investment amount change if the interest rate was 5% instead of 4.1%?
2. What would the future value be if they invested $50,000 instead?
3. How does the frequency of compounding (monthly, annually) affect the required investment?
4. What is the total interest earned on the investment over the 18 years?
5. How would the required investment change if they wanted to achieve the goal in 15 years instead of 18?

**Tip:** The more frequently interest is compounded, the more interest is earned over time!

Learn how to calculate how much money Guyton and Jessica should invest now to reach $79,000 in 18 years for their grandson's college education. This solution uses the compound interest formula, given a 4.1% interest rate compounded quarterly. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation