Final answer:
To calculate the interest earned on a $1,000 investment at 3% annual interest compounded annually after 3 years, the compound interest formula is used. After the calculations, the amount of interest is found to be approximately $92.73.
Step-by-step explanation:
To calculate the amount of interest earned on an investment of $1,000 in a certificate of deposit with a 3.00% interest rate compounded annually after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount ($1,000 in this case)
- 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
We know that r is 3% or 0.03 in decimal form, n is 1 since the interest is compounded annually, and t is 3 years.
Substituting the values, we get:
A = 1000(1 + 0.03/1)^(1*3) = 1000(1 + 0.03)^3 = 1000(1.03)^3
Calculating this gives us:
A ≈ 1000(1.092727) ≈ $1092.73
The interest earned is the future value minus the initial principal:
Interest = A - P = 1092.73 - 1000 = $92.73
Therefore, the interest earned after 3 years is approximately $92.73.