Today Isabella is having her 5th birthday and her parents want to make one single deposit now so they can collect a total of 50000 Brazilian Real when she is 18.
The investment is thought to be for n=13 years.
The present value (PV) and the future value (FV) of the investment can be calculated by using the compound interest's formula:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]Where r is the interest rate (APR) offered by the bank, m is the number of compounding periods by each year. Since the compounding period is monthly, then m=12.
If we are given the final value and we want to calculate the present value, then the formula is:
[tex]PV=FV(1+\frac{r}{m})^{-n\cdot m}[/tex]Substituting:
[tex]PV=50000(1+\frac{0.055}{12})^{-13\cdot12}[/tex]Calculating:
[tex]\begin{gathered} PV=50000(1.0045833)^{-156} \\ PV=50000\cdot0.49 \\ PV=24499.59 \end{gathered}[/tex]Isabella's parents should deposit near 24500 Brazilian Reals today