Question

Suppose I invest $400 in an account that pays 3% interest annually. How much will I have in the account after 2 years, assuming that I make no other deposits or withdrawals?

Equation 1: A = 400(1+.3)^2

Equation 2: A = 400(1+.3)^24

Equation 3: A = 400(1+.03)^2

Equation 4: A = 400(1+.03)^24

Answer 1

To determine how much you will have in the account after 2 years with an investment of $400 at an annual interest rate of 3%, you should use the correct equation.

The correct formula for compound interest is:

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

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).
- \( t \) is the time the money is invested for in years.

In your case:
- \( P = 400 \)
- \( r = 0.03 \) (which is 3% written as a decimal)
- \( t = 2 \)

Thus, the correct equation to use is:

\[ A = 400(1 + 0.03)^2 \]

This corresponds to **Equation 3: A = 400(1+.03)^2**.

Now, let's calculate it:

1. Calculate \( (1 + 0.03) = 1.03 \).
2. Raise it to the power of 2: \( (1.03)^2 = 1.0609 \).
3. Multiply by the principal:

\[ A = 400 \times 1.0609 = 424.36 \]

After 2 years, you will have approximately **$424.36** in the account.