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

1 answer

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.