Final answer:
To determine the amount of interest earned, the formula for compound interest is used. For $5,000 at 15% compounded annually over 10 years, the total interest earned is approximately $15,229 (rounded to the nearest dollar), which is calculated using the compound interest formula and then rounding to the nearest dollar.
Step-by-step explanation:
To find the amount of interest earned on $5,000 at 15% compounded annually for 10 years, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- 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 for in years.
In this case, P = $5,000, r = 0.15 (15%), n = 1 (since the interest is compounded annually), and t = 10 years.
Plugging these numbers into the formula:
A = 5000(1 + 0.15/1)^(1*10) = 5000(1 + 0.15)^10 = 5000 * 4.0457 ≈ $20,228.50
The total interest earned I, can be found by subtracting the principal from the total amount:
I = A - P = $20,228.50 - $5,000 ≈ $15,228.50
Therefore, rounding to the nearest dollar, the interest earned is approximately $15,229, which is not one of the options given but is the correct calculation.