Final answer:
After 20 years of reinvesting $100 at an annual interest rate of 8 percent, you will have approximately $466.10 due to the power of compound interest.
Step-by-step explanation:
If you have $100 to invest at an annual interest rate of 8 percent, and you reinvest the interest payments also at 8 percent for 20 years, you're dealing with a case of compound interest. The general formula for compound interest is A = P(1 + r/n)nt, where:
- P is the principal amount (the initial amount of money)
- 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 or borrowed for, in years
- A is the amount of money accumulated after n years, including interest.
Since the interest is compounded annually, n is 1. Therefore, the formula simplifies to A = P(1 + r)t.
For your specific question, you will use the following values:
- P = $100
- r = 0.08 (8% expressed as a decimal)
- n = 1 (since interest is compounded annually)
- t = 20 years
The calculation will be A = 100(1 + 0.08)20.
Now performing the calculation:
A = 100(1.08)20
A ≈ 100(4.66)
A ≈ $466.10
Therefore, after 20 years, you will have approximately $466.10 available.