Questions: José Martinez, an immigrant from Mexico, estimates that he needs 4,000 to start a (very) small grocery store in 4 years. How much must he deposit today if his credit union will pay 8% compounded quarterly? How much should he deposit today? (Round to the nearest cent as needed.)

Solution Steps

We are given the future value \( FV = 4000 \), the annual interest rate \( r = 0.08 \), the number of compounding periods per year \( n = 4 \), and the time in years \( t = 4 \).

Using the present value formula:

\[ PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}} \]

we substitute the known values:

\[ PV = \frac{4000}{\left(1 + \frac{0.08}{4}\right)^{4 \cdot 4}} \]

Calculating the expression gives us:

\[ PV \approx 2913.7832548569368 \]

Rounding this to the nearest cent, we find:

\[ PV \approx 2913.78 \]

Final Answer