https://file.aiquickdraw.com/mathbot/file/1729532678761lkeqqi2g.jpg

The problem in the image involves calculating the future value of an investment using exponential growth due to compound interest.

### Given information:
- Initial investment $ P = 15,000 $ dollars
- Interest rate $ r = 4.3\% = 0.043 $ per year
- Time $ t = 2031 - 2013 = 18 $ years
- Formula: $ A = P(1 + r)^t $, where:
  - $ A $ is the accrued amount
  - $ P $ is the principal (initial investment)
  - $ r $ is the annual interest rate
  - $ t $ is the number of years

### Solution:
Substitute the values into the formula:
\[
A = 15000(1 + 0.043)^{18}
\]
\[
A = 15000(1.043)^{18}
\]
Now let's calculate the final value.

\[
A = 15000 \times (1.043)^{18} \approx 15000 \times 2.072
\]
\[
A \approx 31080
\]

So, the accrued value in the year 2031 will be approximately **$31,080**.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. What is the formula for continuous compound interest?
2. How would the result change if the interest were compounded monthly instead of annually?
3. What is the difference between simple interest and compound interest?
4. How do inflation rates affect the future value of money?
5. How could Staci invest to reduce the risk of fluctuating interest rates?

**Tip:** Always ensure the interest rate and time period match (e.g., both in years) when applying compound interest formulas.

In 2013, Staci invested $15,000 in a savings account for her newborn son. The account pays 4.3% interest each year. Determine the accrued value of the account in the year 2031, when her son will go to college. Round your answer to the nearest cent.

Learn how to determine the future value of a $15,000 investment growing at 4.3% annual interest, compounded yearly. This step-by-step example calculates the accrued value by 2031, when the son starts college, using the compound interest formula.

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