Question

What are the future value and the interest earned if $3000 is invested for 6 years at 8\% compounded quarterly?

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asked 2021-05-25
What are the future value and the interest earned if \($3000\) is invested for 6 years at \(8\%\) compounded quarterly?

Expert Answers (1)

2021-05-26

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 \(P=3000,\ r=8\%,\ n=4,\ t=6\)
Plugging the values,
Hence the future value is \($4825.31\)
The interest earned is
\(A=P\left(1+\frac{r}{n}\right)^{nt}\)
\(A=(3000)(1+\frac{0.08}{4}^{(4)(6)})\)
\(A=(3000)(1+0.02)^{24}\)
\(A=(3000)(1.02)^{24}\)
\(A=(3000)(1.60844)\)
\(A=4825.31\)
\(I=4825.31-3000=1825.31\)

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