We have an amount that is compounded quarterly for 5 years.
To calculate the future value (FV) of this amount (PV), we have to write:
[tex]FV=PV\cdot(1+\frac{r}{m})^{n\cdot m}[/tex]where:
r: annual interest rate (r=0.05 for 5%).
m: number of subperiods of compounding within a year. In this case, m=4 because it compounds quarterly (every 3 months) and we have 4 quarters in a year.
n: number of periods. In this case, number of years (n=5) as the interest rate is annual.
PV: present value (PV=7000)
Then, we can replace and calculate as:
[tex]\begin{gathered} FV=PV\cdot(1+\frac{r}{m})^{n\cdot m} \\ FV=7000\cdot(1+\frac{0.05}{4})^{5\cdot4} \\ FV=7000\cdot(1+0.0125)^{20} \\ FV=7000\cdot1.0125^{20} \\ FV\approx7000\cdot1.282037 \\ FV\approx8974.26 \end{gathered}[/tex]Answer: the compound amount is $8,974.26.
