 # What are the future value and the interest earned if \$3000 is invested for 6 years at 8\% compounded quarterly? opatovaL 2021-05-25 Answered
What are the future value and the interest earned if $3000$ is invested for 6 years at $8\mathrm{%}$ compounded quarterly?
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The future value of an amount P invested at interest rate r (in decimals), compounded n times per year and for n years is given by:
Here
Plugging the values,
Hence the future value is $4825.31$
The interest earned is
$A=P{\left(1+\frac{r}{n}\right)}^{nt}$
$A=\left(3000\right)\left(1+{\frac{0.08}{4}}^{\left(4\right)\left(6\right)}\right)$
$A=\left(3000\right)\left(1+0.02{\right)}^{24}$
$A=\left(3000\right)\left(1.02{\right)}^{24}$
$A=\left(3000\right)\left(1.60844\right)$
$A=4825.31$
$I=4825.31-3000=1825.31$