Question

Trayne Rice has $3,000 to invest for three years. He wants to receive $5,000 at the end of the three years. What interest rate would his investment have to earn to achieve his goal?

a. 17%
b. 25%
c. 33.33%
d. 50%

Answer 1

To find the interest rate needed to grow a $3,000 investment to $5,000 in three years, we use the future value formula and solve for the interest rate. The calculation revealed that an annual interest rate of approximately 22.22% is required, which was not among the provided options.

Step-by-step explanation:

To determine the interest rate needed for Trayne Rice to achieve his goal of turning a $3,000 investment into $5,000 after three years, we can use the future value formula for simple interest: Future Value = Principal × (1 + (Interest Rate × Time)). In this case, we are solving for the Interest Rate, which is represented as 'r'. Trayne Rice's principal amount is $3,000, his desired future value is $5,000, and the time is three years.

Therefore, the equation to solve is: $5,000 = $3,000 × (1 + (r × 3)). By rearranging the formula, we get r × 3 = ($5,000/$3,000) - 1, which simplifies to r × 3 = 5/3 - 1, or r × 3 = 2/3. Hence, r = (2/3) / 3, which equals 2/9, or approximately 0.2222. After converting to a percentage, this gives us an annual interest rate of roughly 22.22%, which is not one of the options provided in the question, indicating a potential error in the options or the need for Trayne to adjust his expectations.