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 in an account to grow to $60,000 in 18 years at an interest rate of 9% compounded monthly, we can use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest ($60,000).
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal) (9% = 0.09).
- $ n $ is the number of times that interest is compounded per year (monthly = 12).
- $ t $ is the time the money is invested for in years (18).

We need to rearrange the formula to solve for $ P $:

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

Now, substituting the values into the formula:

- $ A = 60,000 $
- $ r = 0.09 $
- $ n = 12 $
- $ t = 18 $

Calculating:

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

Calculating the components step by step:

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} $:

\[
1.0075^{216} \approx 5.48464
\]

4. Finally, substitute back into the formula for $ P $:

\[
P = \frac{60000}{5.48464} \approx 10,947.83
\]

Therefore, the lump sum that parents need to deposit is approximately **$10,947.83**.

Would you like any further details or have any questions about the calculation? Here are some related questions you might consider:

1. How does the frequency of compounding affect the final amount?
2. What would the lump sum be if the interest rate were 6% instead of 9%?
3. How much would the parents need to deposit if they wanted to achieve $80,000 in the same time period?
4. What are some investment options that can yield similar returns?
5. How does inflation impact the value of college funds over 18 years?

**Tip:** Always consider different investment scenarios and rates of return when planning for future expenses.

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 to reach $60,000 for a college fund in 18 years at a 9% interest rate compounded monthly. This guide explains the compound interest formula and its application.

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