What lump sum do parents need to deposit in an account earning 7%, compounded monthly, so that it will grow to $90,000 for their son's college fund in 17 years? (Round your answer to the nearest cent.)


To determine the lump sum that parents need to deposit in an account earning 7% compounded monthly to grow to $90,000 in 17 years, we can use the formula for compound interest:

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

Where:
- $ A $ is the future value of the investment (in this case, $90,000),
- $ P $ is the initial principal (the lump sum we're solving for),
- $ r $ is the annual interest rate (7% or 0.07),
- $ n $ is the number of times the interest is compounded per year (monthly compounding means $ n = 12 $),
- $ t $ is the number of years (17 years).

We are solving for $ P $, the initial deposit:

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

Substituting the known values:

\[
P = \frac{90,000}{\left(1 + \frac{0.07}{12}\right)^{12 \times 17}}
\]

Let's calculate this.The parents need to deposit approximately $27,474.74 in an account earning 7% compounded monthly to grow to $90,000 in 17 years.

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

Here are some related questions:
1. How would the required lump sum change if the interest rate were 6% instead of 7%?
2. What if the parents want the fund to grow to $100,000 instead of $90,000?
3. How does monthly compounding compare to annual compounding in terms of final savings?
4. What if the time frame is 15 years instead of 17 years—how much would the initial deposit be?
5. How would the formula change for continuous compounding?

**Tip:** Compound interest can greatly increase savings over time, especially with higher interest rates and more frequent compounding periods.

What lump sum do parents need to deposit in an account earning 7%, compounded monthly, so that it will grow to $90,000 for their son's college fund in 17 years? (Round your answer to the nearest cent.)

Find out how much parents need to deposit now to grow a college fund to $90,000 in 17 years with a 7% interest rate, compounded monthly. This problem explores compound interest calculations and exponential growth, ideal for high school students in Grades 10-12.

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