In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.8% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.

In the year 2029, the accrued value will be $

We can calculate the accrued value of the savings account using the formula for compound interest:

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

Where:
- $ A $ is the accrued value of the investment (what we want to find),
- $ P = 14,500 $ is the principal (the initial investment),
- $ r = 0.038 $ is the annual interest rate (3.8%),
- $ n = 1 $ since the interest is compounded annually,
- $ t = 2029 - 2011 = 18 $ is the number of years the money is invested.

Plugging in these values:

\[
A = 14,500 \left( 1 + \frac{0.038}{1} \right)^{1 \times 18}
\]

\[
A = 14,500 \left( 1.038 \right)^{18}
\]

Let me calculate this.The accrued value of the account in the year 2029 will be **$28,373.99**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the impact of a higher interest rate on the final accrued value?
2. How would the value change if the interest was compounded monthly instead of annually?
3. What if Staci invested an additional amount each year? How would the formula change?
4. How does compound interest compare to simple interest for the same investment?
5. If the investment were for 25 years instead of 18, how much would the final amount be?

**Tip:** Compounding more frequently (e.g., monthly or daily) results in a higher accrued value over time.

In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.8% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer to the nearest cent.

Learn how to calculate the accrued value of a $14,500 investment with a 3.8% interest rate over 18 years using the compound interest formula. This problem is ideal for students in Grades 9-12 and covers exponential growth and compound interest.

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