In 2011 Staci invested $15,500 in a savings account for her newborn son. The account pays 2.8% 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 $

The problem involves finding the accrued value of an investment with annual interest compounded over several years. This is a straightforward application of the compound interest formula:

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

Where:
- $A$ = the accrued amount (future value)
- $P$ = the principal amount (\$15,500)
- $r$ = the annual interest rate (2.8% or 0.028)
- $n$ = the number of times interest is compounded per year (since it’s not specified, we'll assume it's compounded annually, so $n = 1$)
- $t$ = the time in years (from 2011 to 2029, so $t = 2029 - 2011 = 18$ years)

Now let's plug in the values and calculate.

\[
A = 15,500 \left(1 + \frac{0.028}{1}\right)^{1 \times 18}
\]

\[
A = 15,500 \left(1.028\right)^{18}
\]

Let me compute this.The accrued value of the account in the year 2029 will be approximately **$25,480.49**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What if the interest rate were higher, say 3.5%? How would that affect the accrued value?
2. How would the accrued value change if the interest was compounded quarterly instead of annually?
3. What if Staci made an additional annual contribution to the account? How would the future value change?
4. How does simple interest compare to compound interest in this scenario?
5. What would the accrued value be if the investment period was extended to 30 years?

**Tip:** The more frequently interest is compounded, the greater the accrued amount will be!

In 2011 Staci invested $15,500 in a savings account for her newborn son. The account pays 2.8% 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 $15,500 investment with 2.8% annual interest over 18 years. Using the compound interest formula, find the future value of the account by 2029, suitable for high school students in Grades 9-12.

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