Question

supposed your friend was born, your friends parents deposited $2000 in an account paying 3.5% interest compound monthly. what will the account balance be after 15 years?

Answer 1

If we have a deposit of $2000, invested at an an annual interest rate of 3.5% compounded monthly, we can calculate the final value of that deposit in 15 years as:

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

where:

FV: final value of the deposit.

PV: initial deposit (PV = 2000)

r: annual interest rate (r = 0.035)

m: subperiod (as the compound is monthly, and there are 12 months in a year, we have m = 12).

n: period (n=15)

Then, the expression gives us a value of:

`\begin{gathered} FV=PV(1+(r)/(m))^(m\cdot n) \\ FV=2000(1+(0.035)/(12))^(12\cdot15) \\ FV\approx2000(1.002917)^(180) \\ FV\approx2000\cdot1.689 \\ FV\approx3378 \end{gathered}`

Answer: the account balance after 15 years will be $3378.