https://file.aiquickdraw.com/mathbot/file/1727315911373vp6pgwyv.jpg

The question in the image asks: 

"What lump sum investment will grow to $69,000 in 14 years if it is invested at 10%, compounded annually?"

### Formula to Use: 
This is a compound interest problem, and the formula for calculating the future value is:

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

Where:
- $A$ is the amount of money accumulated after $n$ years, including interest.
- $P$ is the principal amount (the initial lump sum).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year (for annual compounding, $n = 1$).
- $t$ is the time the money is invested for, in years.

Here:
- $A = 69,000$
- $r = 0.10$ (10%)
- $n = 1$ (since interest is compounded annually)
- $t = 14$ years

We are solving for $P$ (the lump sum investment). Re-arranging the formula for $P$:

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

Let me calculate that for you.The initial lump sum investment needed to grow to $69,000 in 14 years at an annual interest rate of 10%, compounded annually, is approximately **$18,169.86**.

Would you like more details or have any questions?

Here are some related questions for practice:
1. What would the lump sum be if the interest rate was 8%?
2. How much would the investment be worth after 20 years at 10% interest?
3. What is the future value of $20,000 invested at 10% for 14 years?
4. How does quarterly compounding affect the required lump sum?
5. How much interest is earned over the 14 years?

**Tip**: Always double-check whether the interest is compounded annually, quarterly, or monthly, as it affects the total amount.

What lump sum investment will grow to $69,000 in 14 years if it is invested at 10%, compounded annually?

Learn how to calculate the initial lump sum investment required to grow to $69,000 in 14 years, given a 10% annual interest rate compounded annually. This problem involves the use of compound interest formulas and is suitable for Grades 10-12.

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