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If a savings account of $10,000 is compounded semi-annually at 19.82% annual interest, how much will the account be worth in 54 months? Round your answer tothe nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.

Respuesta :

Using the compound interest formula:

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

Where:

A = Amount

P = Principal

r = interest rate

n = Number of times the interest is compounded per year

t = time

so:

[tex]\begin{gathered} r=0.1982 \\ P=10000 \\ n=2 \\ t=54_{\text{ }}weeks\times\frac{1year}{52weeks}=\frac{27}{26} \end{gathered}[/tex][tex]\begin{gathered} A=10000(1+\frac{0.1982}{2})^{2\cdot\frac{27}{26}} \\ A\approx12168.33 \end{gathered}[/tex]

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