Question

A newborn child receives a $6,000 gift toward a college education from her grandparents. How much will the $6,000 be worth in 19 years if it is invested at 7.8%compounded quarterly?

Answer 1

Solution:

To find the amount after 19 years, we use the compound interest formula.

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where;} \\ A\text{ is the amount after t-years} \\ P\text{ is the principal or initial deposit} \\ r\text{ is the rate} \\ n\text{ is the number of compounding} \\ t\text{ is the time } \end{gathered}$

Given:

$\begin{gathered} P=\text{ \ 6000} \\ t=19\text{years} \\ r=7.8\text{ \% =}\frac{7.8}{100}=0.078 \\ n=4\text{ (compounded quarterly)} \end{gathered}$

Substituting these values into the formula;

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=6000(1+\frac{0.078}{4})^{4\times19} \\ A=6000(1+0.0195)^{76} \\ A=6000(1.0195)^{76} \\ A=6000\times1.0195^{76} \\ A=26,036.39 \end{gathered}$

Therefore, the amount $6,000 will be worth in 19 years if it is invested at 7.8% compounded quarterly is $26,036.39