Final answer:
Using the compound interest formula, A = P(1 + r/n)^(nt), and substituting the values given, the future value of $600 at 4% compound interest over 3 years is approximately $674.92.
Step-by-step explanation:
You have $600 in the bank at a 4% compound interest rate over 3 years. To calculate the total amount you'll have at the end of this period, we'll use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($600).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Assuming that the interest is compounded once a year (n = 1), we substitute the values into the formula:
A = 600(1 + 0.04/1)^(1*3)
A = 600(1.04)^3
A = 600 * 1.124864
A ≈ $674.92
Therefore, after 3 years, you'll have approximately $674.92 in your bank account from the initial $600 investment with compound interest.