Question

Calculate the compound amount when $7000 is deposited in an account earning 5% interest, compounded quarterly, for 5 years. (Round your answer to two decimal places.)$

Answer 1

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:

`FV=PV\cdot(1+(r)/(m))^(n\cdot m)`

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:

`\begin{gathered} FV=PV\cdot(1+(r)/(m))^(n\cdot m) \\ FV=7000\cdot(1+(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}`

Answer: the compound amount is $8,974.26.