Questions: What is the simple interest rate on a 1500 investment paying 1,012.50 interest in 13.5 years? % (round to the nearest tenth of a percent)

Solution Steps

To find the simple interest rate, we can use the formula for simple interest:

$$I = P \times r \times t$$

where:

• $I$ is the interest earned,
• $P$ is the principal amount,
• $r$ is the rate of interest per year,
• $t$ is the time in years.

We need to solve for $r$:

$$r = \frac{I}{P \times t}$$

Given:

• $I = 1012.50$
• $P = 1500$
• $t = 13.5$

We can plug these values into the formula to find $r$ and then convert it to a percentage.

We are given the following values:

• Principal amount, $P = 1500$
• Interest earned, $I = 1012.50$
• Time in years, $t = 13.5$

The formula for simple interest is given by:

$$I = P \times r \times t$$

We need to solve for the interest rate $r$:

$$r = \frac{I}{P \times t}$$

Substituting the known values into the formula:

$$r = \frac{1012.50}{1500 \times 13.5}$$

Calculating $r$:

$$r = \frac{1012.50}{20250} = 0.05$$

To express $r$ as a percentage:

$$\text{Interest Rate} = r \times 100 = 0.05 \times 100 = 5.0\%$$

Final Answer