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