Question

Sharon Nguyen has $25,000 to invest and believes that she can earn 8% compounded semiannually. Find the amount if she invests for 10 years

Answer 1

Given:

`\begin{gathered} P=\text{ \$25,000} \\ r=8\text{ \%}=(8)/(100)=0.08 \\ t=10\text{years} \\ n=\text{twice a year(semiannually),}n=2 \end{gathered}`

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

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

Substituting the given values into the formula,

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=25000(1+(0.08)/(2))^(2*10) \\ A=25000(1+0.04)^(20) \\ A=25000(1.04)^(20) \\ A=25000*1.04^(20) \\ A=\text{ \$54,778.08} \end{gathered}`

Therefore, the amount after 10 years is $54,778.08