Arnett College predicts that in 1818 years it will take $350,000$⁢350,000 to attend the college for four years. Hannah has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Hannah put aside in an account with an APR of 8%8% compounded monthly in order to have $350,000$⁢350,000 in the account in 1818 years? Round your answer to the nearest cent, if necessary.


To determine how much Hannah should invest now, we need to use the formula for compound interest, specifically the future value formula:

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

Where:
- $ A $ is the future value (the amount Hannah wants in the future), which is \$350,000.
- $ P $ is the present value (the amount Hannah should invest now).
- $ r $ is the annual interest rate (8% or 0.08 as a decimal).
- $ n $ is the number of times the interest is compounded per year (monthly compounding means $ n = 12 $).
- $ t $ is the number of years (18 years).

We need to solve for $ P $, the present value. Rearranging the formula:

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

Now, let's plug in the values:

- $ A = 350,000 $
- $ r = 0.08 $
- $ n = 12 $
- $ t = 18 $

\[
P = \frac{350,000}{\left(1 + \frac{0.08}{12}\right)^{12 \times 18}}
\]

I'll calculate this.Hannah should invest approximately \$83,321.94 today in an account with an 8% APR, compounded monthly, in order to have \$350,000 in 18 years.

Would you like further clarification, or do you have any other questions? 

Here are five related questions you might find interesting:
1. What if the APR was compounded quarterly instead of monthly?
2. How would the amount change if the interest rate was 6% instead of 8%?
3. How much interest will the investment earn over the 18 years?
4. What if Hannah wanted to make monthly contributions instead of a lump sum?
5. How much would be required if the time frame was extended to 20 years instead of 18?

**Tip**: The more frequently the interest compounds, the more the initial investment grows over time.

Arnett College predicts that in 18 years it will take $350,000 to attend the college for four years. Hannah has a substantial amount of cash and wishes to invest a lump sum of money for her child’s college fund. How much should Hannah put aside in an account with an APR of 8% compounded monthly in order to have $350,000 in the account in 18 years? Round your answer to the nearest cent, if necessary.

Learn how to calculate the lump sum investment required to accumulate $350,000 for college in 18 years with an 8% APR compounded monthly. This problem covers key financial concepts like compound interest and the present value formula, 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