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

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03-11-2022
Mathematics

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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

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Solution:

Given:

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

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

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

Substituting the given values into the formula,

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=25000(1+\frac{0.08}{2})^{2\times10} \\ A=25000(1+0.04)^{20} \\ A=25000(1.04)^{20} \\ A=25000\times1.04^{20} \\ A=\text{ \$54,778.08} \end{gathered}[/tex]

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

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