Final answer:
To find the interest earned on $20,000 invested for 5 years at 6% interest compounded annually, use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. The interest earned is the difference between the final amount and the initial investment.
Step-by-step explanation:
To find the interest earned on $20,000 invested for 5 years at 6% interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial investment).
- r is the annual interest rate (in decimal form).
- n is the number of times that interest is compounded per year.
- t is the number of years the money is invested for.
Plugging in the values from the question, we have:
A = 20000(1 + 0.06/1)^(1*5)
A = 20000(1 + 0.06)^5
A = 20000(1.06)^5
A ≈ 20000(1.338225)
A ≈ 26764.50
The interest earned is the difference between the final amount and the initial investment:
Interest = A - P
Interest = 26764.50 - 20000
Interest ≈ $6,764.50