Question

Tom wants to save $50,000 for his business in five years. If his savings account earns 4% interest compounded annually, how much should he approximately deposit now?
A.$40,000
B.$42,000
C.$45,000
D.$47,000

Answer 1

To determine how much Tom needs to deposit now to reach his goal of $50,000 in five years with an interest rate of 4% compounded annually, we can use the formula for the present value (PV) of a future amount (FV):

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

where:
- \(FV\) is the future value ($50,000),
- \(r\) is the interest rate (0.04),
- \(n\) is the number of years (5).

Plugging in the values:

\[
PV = \frac{50000}{(1 + 0.04)^5}
\]

Calculating \((1 + 0.04)^5\):

\[
(1.04)^5 \approx 1.21665
\]

Now substitute back into the present value formula:

\[
PV = \frac{50000}{1.21665} \approx 41,050.12
\]

This means Tom should deposit approximately $41,050.12 now.

Looking at the options provided:

A. $40,000
B. $42,000
C. $45,000
D. $47,000

The closest option is **B. $42,000**.