We have to calculate the present value of an investment so that we get a future value of $20,000.
The number of periods is n = 10 years, compounded quarterly (m = 4 subperiods per year).
The annual interest rate is 3% (r = 0.03).
Then, we can express the present value PV as:
[tex]PV=\frac{FV}{(1+\frac{r}{m})^{n\cdot m}}[/tex]We replace with the values and calculate as:
[tex]\begin{gathered} PV=\frac{20000}{(1+\frac{0.03}{4})^{10\cdot4}} \\ PV=\frac{20000}{1.0075^{40}} \\ PV\approx\frac{20000}{1.34835} \\ PV\approx14832.96 \end{gathered}[/tex]Answer: You will need to deposit $14,832.96.
