Questions: An investment of 6000 was made 5 years ago and has grown to 7,500. What is the annual simple interest rate of this investment?

Solution Steps

To find the annual simple interest rate, we can use the formula for simple interest: \[ A = P(1 + rt) \] 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, and \( t \) is the time the money is invested for in years. We need to solve for \( r \).

1. Identify the given values: \( P = 6000 \), \( A = 7500 \), and \( t = 5 \).
2. Rearrange the simple interest formula to solve for \( r \).
3. Substitute the given values into the formula and solve for \( r \).

We are given the following values:

• Principal amount \( P = 6000 \)
• Amount after 5 years \( A = 7500 \)
• Time period \( t = 5 \)

The formula for the amount accumulated with simple interest is given by: \[ A = P(1 + rt) \] We need to rearrange this formula to solve for the annual interest rate \( r \): \[ r = \frac{A}{P} - 1 \quad \text{and then} \quad r = \frac{A/P - 1}{t} \]

Substituting the known values into the rearranged formula: \[ r = \frac{7500 / 6000 - 1}{5} \] Calculating \( \frac{7500}{6000} \): \[ \frac{7500}{6000} = 1.25 \] Thus, \[ r = \frac{1.25 - 1}{5} = \frac{0.25}{5} = 0.05 \]

To express \( r \) as a percentage, we multiply by 100: \[ r \times 100 = 0.05 \times 100 = 5.00\% \]

Final Answer