Questions: How much time would it take to earn 61 simple interest on an investment of 790 if the annual rate of return was 3.5% ? It would take years. Round your answer to the nearest tenth of a year.

Solution Steps

To find the time it takes to earn a specific amount of simple interest, 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 annual interest rate (as a decimal), and \( t \) is the time in years. We need to solve for \( t \) by rearranging the formula to \( t = \frac{I}{P \times r} \).

We are given the following values:

• Interest earned, \( I = 61 \)
• Principal amount, \( P = 790 \)
• Annual interest rate, \( r = 3.5\% = 0.035 \)

The formula for simple interest is given by: \[ I = P \times r \times t \] To find the time \( t \), we rearrange the formula: \[ t = \frac{I}{P \times r} \]

Substituting the known values into the equation: \[ t = \frac{61}{790 \times 0.035} \]

Calculating the denominator: \[ 790 \times 0.035 = 27.65 \] Now substituting back: \[ t = \frac{61}{27.65} \approx 2.2061 \]

Rounding \( t \) to the nearest tenth: \[ t \approx 2.2 \]

Final Answer