To calculate the future value of an investment with a fixed annual interest rate, you can use the formula for compound interest:
Future Value (FV) = P (1 + r)^t
Where:
- FV: Future Value of the investment
- P: Principal amount (initial investment)
- r: Annual interest rate (as a decimal)
- t: Number of years the money is invested
In this case, the principal amount is $100, the annual interest rate is 11% (or 0.11 as a decimal), and the investment period is 10 years. Plugging these values into the formula gives us:
FV = 100 (1 + 0.11)^10
First, calculate (1 + 0.11):
1 + 0.11 = 1.11
Next, raise 1.11 to the power of 10:
1.11^10 ≈ 2.83942
Now, multiply this result by the principal amount:
FV ≈ 100 * 2.83942 ≈ 283.94
So, after 10 years, your $100 investment earning 11% interest per year will grow to approximately $283.94.
This demonstrates the power of compound interest, showing how a relatively small initial investment can grow significantly over time.