What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $60,000 for their son’s college fund in 18 years? (Round your answer to the nearest cent.)

To find the lump sum $ P $ that parents need to deposit, we can use the future value formula for compound interest:

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

Where:
- $ FV $ is the future value ($60,000).
- $ r $ is the annual interest rate (0.09).
- $ n $ is the number of times interest is compounded per year (12 for monthly).
- $ t $ is the number of years the money is invested (18).

We need to solve for $ P $:

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

Substituting in the values:

\[
P = \frac{60000}{\left(1 + \frac{0.09}{12}\right)^{12 \times 18}}
\]

Calculating the components:

1. Calculate $ \frac{r}{n} = \frac{0.09}{12} = 0.0075 $.
2. Calculate $ nt = 12 \times 18 = 216 $.
3. Calculate $ \left(1 + 0.0075\right)^{216} $.

Now, calculating it step by step:

\[
1 + 0.0075 = 1.0075
\]
\[
(1.0075)^{216} \approx 4.5356
\]
\[
P \approx \frac{60000}{4.5356} \approx 13263.66
\]

Therefore, the lump sum needed is approximately **$13,263.66**.

If you have any questions or need further details, let me know! Here are some related questions you might consider:

1. How does the choice of compounding frequency affect the final amount?
2. What would the required lump sum be if the interest rate were lower, say 6%?
3. How much would the parents need to save monthly instead of as a lump sum?
4. What is the impact of inflation on the future value needed for college?
5. How can they adjust their investment strategy if the rate changes after a few years?

**Tip:** Consider opening a separate savings account dedicated to this goal to avoid spending the funds unintentionally.

What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $60,000 for their son’s college fund in 18 years?

Discover how to calculate the lump sum needed for a college fund to reach $60,000 in 18 years at an interest rate of 9% compounded monthly. This guide explores compound interest formulas and provides step-by-step solutions suitable for high school students.

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