Question

Sharon Nguyen has $25,000 to invest and believes that she can earn 6% compounded semiannually. Find the compound amount if she invests for 2 years

Answer 1

Solution:

Given:

$\begin{gathered} P=\text{ \ 25,000} \\ r=\text{ 6\%}=\frac{6}{100}=0.06 \\ n=2(compounded\text{ semiannually)} \\ t=2\text{years} \end{gathered}$

To get the compound amount, we use the amount formula;

$A=P(1+\frac{r}{n})^{nt}$

Substituting the values given into the formula,

$\begin{gathered} A=25000(1+\frac{0.06}{2})^{2\times2} \\ A=25000(1+0.03)^4 \\ A=25000(1.03)^4 \\ A=25000\times1.03^4 \\ A=28137.72 \\ \\ \text{Hence,} \\ A=\text{ \ 28137.72} \end{gathered}$

Therefore, the compound amount, if she invests for 2 years, is $28137.72