To determine how much Tom should deposit now to reach $50,000 in five years with an annual interest rate of 4%, we can use the formula for the present value \( P \):
\[ P = \frac{A}{(1 + r)^n} \]
Where:
- \( A \) is the amount of money to be accumulated in the future ($50,000),
- \( r \) is the annual interest rate (4% or 0.04),
- \( n \) is the number of years the money is invested (5 years).
Substituting in the values we have:
\[ P = \frac{50000}{(1 + 0.04)^5} \]
Calculating \( (1 + 0.04)^5 \):
\[ (1 + 0.04)^5 = (1.04)^5 \approx 1.2166529 \]
Now, substituting that value back into the equation for \( P \):
\[ P = \frac{50000}{1.2166529} \approx 41000.51 \]
This means that Tom should deposit approximately $41,000 now.
Looking at the provided options:
A. $40,000
B. $42,000
C. $45,000
D. $47,000
The closest option to $41,000 is A. $40,000. So, the best approximate answer is:
A. $40,000.