Respuesta :
We have an investment with present value PV that will have a future value FV = 4000 after n=5 years.
The APR is 6% and is compounded monthly.
As the APR does not take into account this compounding, we can write the FV in function of the present value as:
[tex]FV=PV\cdot(1+\frac{r}{m})^{n\cdot m}[/tex]where r: APR, m: number of subperiods (m=12) and n: number of periods (n=5).
Then, we can replace the values and calculate PV as:
[tex]\begin{gathered} FV=PV\cdot(1+\frac{r}{m})^{n\cdot m} \\ 4000=PV\cdot(1+\frac{0.06}{12})^{5\cdot12} \\ 4000=PV\cdot(1+0.005)^{60} \\ 4000=PV\cdot1.005^{60} \\ PV=\frac{4000}{1.005^{60}} \\ PV\approx\frac{4000}{1.3489} \\ PV\approx2965.49 \end{gathered}[/tex]Answer:
Present value = $2965.49.
This means that to have an investment worth $ 4000 in the future, you must invest $ 2965.49 now, compounding monthly, assuming the APR is 6% and constant over the next five years.
