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:
[tex]FV=PV(1+\frac{r}{m})^{m\cdot n}[/tex]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:
[tex]\begin{gathered} FV=PV(1+\frac{r}{m})^{m\cdot n} \\ FV=2000(1+\frac{0.035}{12})^{12\cdot15} \\ FV\approx2000(1.002917)^{180} \\ FV\approx2000\cdot1.689 \\ FV\approx3378 \end{gathered}[/tex]Answer: the account balance after 15 years will be $3378.
