Question

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

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

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
$$A=P\left(1+\frac{r}{n}\right)^{nt}$$
$$A=(3000)(1+\frac{0.08}{4}^{(4)(6)})$$
$$A=(3000)(1+0.02)^{24}$$
$$A=(3000)(1.02)^{24}$$
$$A=(3000)(1.60844)$$
$$A=4825.31$$
$$I=4825.31-3000=1825.31$$