Final answer:
To find the annual interest rate, you can use the formula for the future value of an ordinary annuity. By plugging in the given values and solving the equation, you can determine that the required annual interest rate is 8.12%.
Step-by-step explanation:
To find the annual interest rate you need to earn on your investment, we can use the formula for the future value of an ordinary annuity: FV = P(1 + r)^n, where FV is the future value, P is the investment amount, r is the interest rate per period, and n is the number of periods.
In this case, you are given that the investment amount is $2,000, the future value is $30,000, and the number of periods is 10 years. Let's plug in these values into the formula: $30,000 = $2,000(1 + r)^10.
Simplifying the equation, we get (1 + r)^10 = 30,000/2,000 = 15. Taking the 10th root of both sides, we get 1 + r = 15^(1/10). Subtracting 1 from both sides, we get r = 15^(1/10) - 1.
Calculating the value of 15^(1/10) - 1 using a calculator, we find that r is approximately 0.0812, or 8.12% (rounded to two decimal places). Therefore, you must earn an annual interest rate of 8.12% on your investment in order to have $30,000 after 10 years.