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=(FV)/((1+(r)/(m))^(n\cdot m))`

We replace with the values and calculate as:

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

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