Question

If you receive \(\$ 500\) in simple interest on a loan that you made for \(\$ 10,000\) for five years, what was the interest rate you charged?

Short answer

The interest rate charged on the loan was \(1\%\) per year.

Step-by-step solution

Write down the simple interest formula

We need to use the simple interest formula to find the interest rate (R). The formula is: Simple Interest (SI) = Principal (P) × Interest Rate (R) × Time (T)

Substitute the given values into the formula

We know the values for SI, P, and T. We will substitute these values into the formula: \(500 = \)10,000 \times R \times 5$

Solve for the interest rate (R)

Our goal is to find the value of R. First, we will divide both sides of the equation by the product of the principal (P) and time (T): R = \(\frac{500}{10,000 \times 5}\) Now, simplify: R = \(\frac{500}{50,000}\)

Calculate the interest rate as a percentage

To find the interest rate as a percentage, we will multiply R by 100: Interest Rate = R × 100 Interest Rate = \(\frac{500}{50,000} \times 100\) Interest Rate = 0.01 × 100 Interest Rate = 1% The interest rate charged on the loan was 1% per year.