What lump sum do parents need to deposit in an account earning 14%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 12 years? (Round your answer to the nearest cent.)


To solve this problem, 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 (\$100,000 in this case).
- $P$ is the principal (initial deposit), which we need to find.
- $r$ is the annual interest rate (14% or 0.14).
- $n$ is the number of times the interest is compounded per year (12 times for monthly compounding).
- $t$ is the number of years the money is invested (12 years).

Rearranging the formula to solve for $P$:

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

Now we can substitute the values:

\[
P = \frac{100,000}{\left(1 + \frac{0.14}{12}\right)^{12 \times 12}}
\]

Let me calculate this.The parents need to deposit approximately **$18,819.52** in the account for it to grow to $100,000 in 12 years, given a 14% annual interest rate compounded monthly.

Would you like any further details or clarification on this solution?

Here are 5 related questions to explore:
1. How would the required deposit change if the interest rate was 10% instead of 14%?
2. What if the interest was compounded quarterly instead of monthly?
3. How does compounding frequency affect the growth of an investment?
4. How much would the amount grow if they left the money in for 15 years instead of 12?
5. What is the difference between simple interest and compound interest?

**Tip:** Increasing the compounding frequency (e.g., monthly vs. annually) typically results in a higher final amount due to more frequent interest calculations.

What lump sum do parents need to deposit in an account earning 14%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 12 years? (Round your answer to the nearest cent.)

Discover how much parents need to deposit today to accumulate $100,000 for their son's college fund in 12 years with a 14% annual interest rate compounded monthly. This problem involves using the compound interest formula and exponential growth, making it ideal for high school students in Grades 10-12.

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