Final answer:
The investment of $4000 at a 3% annual compound interest rate will be worth $4120 at the end of one year, with $120 earned as compound interest.
Step-by-step explanation:
To calculate the future value of an investment with compound interest calculated yearly, you use the compound interest formula:
Future Value = Principal × (1 + interest rate)time
In this case, the principal is $4000, the rate is 3% (or 0.03 when expressed as a decimal), and the time is 1 year. Placing these values into the formula gives us:
Future Value = $4000 × (1 + 0.03)1
Future Value = $4000 × 1.03
Future Value = $4120
Therefore, at the end of one year, the investment will be worth $4120.
The compound interest earned can be calculated by subtracting the principal from the future value:
Compound interest = Future Value - Principal
Compound interest = $4120 - $4000
Compound interest = $120
So, the investment has earned $120 in compound interest over the year.