Questions: After 8 years, Sheila's account earned 900 in interest. If the interest rate (in decimal form) is 0.08 , how much did Sheila initially invest?

Solution Steps

To find out how much Sheila initially invested, we need to use the formula for simple interest, which is \( I = P \times r \times t \), where \( I \) is the interest earned, \( P \) is the principal amount (initial investment), \( r \) is the interest rate, and \( t \) is the time in years. We need to solve this formula for \( P \).

1. Rearrange the formula to solve for \( P \): \( P = \frac{I}{r \times t} \).
2. Substitute the known values into the formula: \( I = 900 \), \( r = 0.08 \), and \( t = 8 \).

The formula for simple interest is given by: \[ I = P \times r \times t \] where:

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

To find the initial investment \( P \), rearrange the formula: \[ P = \frac{I}{r \times t} \]

Substitute the given values into the formula:

• \( I = 900 \)
• \( r = 0.08 \)
• \( t = 8 \)

\[ P = \frac{900}{0.08 \times 8} \]

Perform the calculation: \[ P = \frac{900}{0.64} = 1406.25 \]

Final Answer