Questions: Use the simple interest formula to determine the missing value. p= 964.77, r=3.5 %, t=?, i= 101.30 t= years (Do not round until the final answer. Then round to the nearest whole number as needed.)

Solution Steps

To determine the missing value \( t \) (time in years) using the simple interest formula, we can use the formula: \[ I = P \times r \times t \] where:

• \( I \) is the interest earned,
• \( P \) is the principal amount,
• \( r \) is the annual interest rate (in decimal form),
• \( t \) is the time in years.

We need to solve for \( t \): \[ t = \frac{I}{P \times r} \]

We are given the following values:

• Principal amount \( P = 964.77 \)
• Annual interest rate \( r = 3.5\% = 0.035 \)
• Interest earned \( I = 101.30 \)

The simple interest formula 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: \[ t = \frac{101.30}{964.77 \times 0.035} \]

Calculating the denominator: \[ 964.77 \times 0.035 = 33.77195 \] Now substituting back: \[ t = \frac{101.30}{33.77195} \approx 2.999974827457025 \]

Rounding \( t \) to the nearest whole number gives: \[ t \approx 3 \]

Final Answer