In 2014 Staci invested $14,000 in a savings account for her newborn son. The account pays 4.7% interest each year. Determine the accrued value of the account in the year 2032, when her son will go to college. Round your answer the nearest cent.


In the year 2032, the accrued value will be $x

The accrued value of an investment in a savings account that pays interest can be calculated using the compound interest formula:

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

Where:
- $ A $ is the accrued value (final amount) of the investment,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time the money is invested for in years.

Since no compounding period is specified, we will assume the interest is compounded annually (which means $ n = 1 $).

Given:
- $ P = 14,000 $,
- $ r = 4.7\% = 0.047 $,
- $ t = 2032 - 2014 = 18 $ years,
- $ n = 1 $.

Now, we can calculate the accrued value $ A $.

\[
A = 14,000 \left(1 + \frac{0.047}{1}\right)^{1 \times 18}
\]

Let’s calculate this.The accrued value of the savings account in the year 2032 will be **$32,001.35**.

Do you have any questions or would you like further details?

Here are 5 related questions to expand on this topic:
1. How would the accrued value change if the interest were compounded quarterly?
2. What if the interest rate increased to 5%?
3. How much interest is earned in total over the 18 years?
4. What would the final amount be if the investment duration was only 15 years?
5. How would the accrued value differ if Staci had invested $20,000 instead of $14,000?

**Tip:** The more frequently interest is compounded, the higher the accrued value will be due to the effect of compounding on the interest itself.

In 2014 Staci invested $14,000 in a savings account for her newborn son. The account pays 4.7% interest each year. Determine the accrued value of the account in the year 2032, when her son will go to college. Round your answer the nearest cent.

Discover how to calculate the accrued value of a $14,000 investment in a savings account at 4.7% interest annually, compounded over 18 years. The detailed solution includes the compound interest formula and step-by-step calculations, providing insights into financial mathematics concepts. Suitable for students in Grades 10-12.

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