Rosa wants to invest \( \$ 4400 \) in a savings account that pays \( 7.1 \% \) simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

To determine how long it will take for Rosa's investment to double in value with simple interest, we can use the formula for simple interest: \[ A = P(1 + rt) \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( t \) is the time the money is invested for in years. In this case: - \( P = 4400 \) - \( A = 2 \times 4400 = 8800 \) (since we want to double the investment) - \( r = 7.1\% = 0.071 \) We need to solve for \( t \): \[ 8800 = 4400(1 + 0.071t) \] Now, let's simplify and solve for \( t \): 1. Divide both sides by \( 4400 \): \[ 2 = 1 + 0.071t \] 2. Subtract 1 from both sides: \[ 1 = 0.071t \] 3. Divide both sides by \( 0.071 \): \[ t = \frac{1}{0.071} \] Now, let's calculate \( t \). Calculate the value by following steps: - step0: Calculate: \(\frac{1}{0.071}\) - step1: Convert the expressions: \(\frac{1}{\frac{71}{1000}}\) - step2: Multiply by the reciprocal: \(\frac{1000}{71}\) Calculating \( t \): \[ t \approx 14.084507 \] Rounding this to the nearest tenth, we find: \[ t \approx 14.1 \] Thus, it will take approximately **14.1 years** for Rosa's investment to double in value at a simple interest rate of \( 7.1\% \).