Question

Solve the problem. The account has quarterly compounding and an APR of 3%. How much would you need to deposit now toreach your $20,000 goal in 10 years?

Answer 1

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:

$PV=\frac{FV}{(1+\frac{r}{m})^{n\cdot m}}$

We replace with the values and calculate as:

$\begin{gathered} PV=\frac{20000}{(1+\frac{0.03}{4})^{10\cdot4}} \\ PV=\frac{20000}{1.0075^{40}} \\ PV\approx\frac{20000}{1.34835} \\ PV\approx14832.96 \end{gathered}$

Answer: You will need to deposit $14,832.96.