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?

Answer 1

To determine how much Tom needs to deposit now to reach his goal of $50,000 in five years with an annual interest rate of 4%, we can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

In this scenario, we need to solve for \( P \):

\[
P = \frac{A}{(1 + r)^n}
\]

Given:
- \( A = 50,000 \)
- \( r = 0.04 \)
- \( n = 5 \)

Substituting these values into the formula, we get:

\[
P = \frac{50000}{(1 + 0.04)^5}
\]
\[
P = \frac{50000}{(1.04)^5}
\]
\[
P = \frac{50000}{1.216652902}
\]
\[
P \approx \frac{50000}{1.2167}
\]
\[
P \approx 41,000.30
\]

Therefore, Tom should approximately deposit **$41,000.30** now to accumulate $50,000 in five years at an interest rate of 4% compounded annually.