Question

In 2011 Staci invested $13,000 in a savings account for her newborn son. The account pays 3.6% 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 $

Answer 1

To solve this problem, we can use the compound interest formula

`A=P(1+(r)/(n))^(nt)`

Where A represents the accrued value, P represents the invested value, r represents the interest(in decimals), n represents the amount of times the interest is compounded per unit 't' and t represents the time.

Since the unit of the time 't' is years, and the interest is compounded yearly, n = 1.

To write a percentage as a decimal, we just have to divide the percentage value by 100.

`3.6\%=0.036`

To find the amount of time t, we just have to subtract the year the money was invested from the year we want to know the money accrued.

`t=2029-2011=18`

Then, using those values on the formula, we have

`\begin{gathered} A=13,000(1+0.036)^6 \\ A=16073.1828298\ldots\approx16073.18 \end{gathered}`

The accrued value in the year 2029 will be $16,073.18.