Rosa wants to invest \( \$ 4800 \) in a savings account. Determine the interest rate (simple interest) required for Rosa 's investment to double in value in 12 years. Round your answer to the nearest tenth of a percent.

To determine the interest rate required for Rosa's investment to double in value in 12 years using 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 (in decimal). - \( t \) is the time the money is invested for in years. In this case: - \( P = 4800 \) - \( A = 2 \times P = 2 \times 4800 = 9600 \) - \( t = 12 \) We need to find \( r \). Plugging in the values we have: \[ 9600 = 4800(1 + 12r) \] Now, let's solve for \( r \) step by step. 1. Divide both sides by 4800: \[ 2 = 1 + 12r \] 2. Subtract 1 from both sides: \[ 1 = 12r \] 3. Divide both sides by 12: \[ r = \frac{1}{12} \] Now, we will convert \( r \) into a percentage by multiplying by 100: \[ r = \frac{1}{12} \times 100 \] Now, let's calculate this value. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{12}\times 100\) - step1: Reduce the numbers: \(\frac{1}{3}\times 25\) - step2: Multiply: \(\frac{25}{3}\) Calculating \( r \) gives us: \[ r = \frac{25}{3} \approx 8.33 \] Thus, the interest rate \( r \) is approximately \( 8.33\% \). Rounding to the nearest tenth of a percent, the required interest rate for Rosa's investment to double in value in 12 years is: \[ \boxed{8.3\%} \]