Ryan invests a sum of money in a savings
account with a fixed annual interest rate of
4.31% compounded Monthly. After 10
years, the balance reaches
$12,855.94. What was the amount of the
initial investment?

To find the initial investment amount $ P $, we'll use the formula for compound interest:

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

Where:
- $ A $ is the amount after $ t $ years (the future value),
- $ P $ is the initial principal (the initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years the money is invested.

Given:
- $ A = 12,855.94 $ (the amount after 10 years),
- $ r = 4.31\% = 0.0431 $,
- $ n = 12 $ (since the interest is compounded monthly),
- $ t = 10 $ years.

We need to find $ P $. Rearranging the compound interest formula to solve for $ P $:

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

Substituting the given values:

\[
P = \frac{12,855.94}{\left(1 + \frac{0.0431}{12}\right)^{12 \times 10}}
\]

Let's calculate that.The initial investment amount was approximately **$8,361.00**.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:
1. How does the compounding frequency affect the final amount?
2. What would the initial investment be if the interest rate were higher?
3. How much interest would Ryan earn after 10 years if compounded annually instead of monthly?
4. How does the compound interest formula differ from simple interest?
5. How long would it take for the investment to double at this interest rate?

**Tip:** Regularly monitoring your investments and understanding how interest is compounded can significantly impact your financial planning.

Learn how to calculate the initial investment using compound interest. Given an amount of $12,855.94 after 10 years at an annual interest rate of 4.31% compounded monthly, find the initial investment amount using the compound interest formula. Suitable for high school students studying financial mathematics.

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