Waiting period. Jamal is waiting to be a millionaire. He wants to know how long he must wait if a. he invests \( \$ 27,523.17 \) at \( 20 \% \) today? b. he invests \( \$ 54,955.85 \) at \( 13 \% \) today? c. he invests \( \$ 126,545.56 \) at \( 11 \% \) today? d. he invests \( \$ 284,998.58 \) at 796 today? 20 years (Round to the nearest whole number.) b. How long will Jamal have to wait to become a millionaire if he invests \( \$ 54,955.85 \) at \( 13 \% \) today? \( \square \) years (Round to the nearest whole number.)

To determine how long Jamal needs to wait to become a millionaire by investing \$54,955.85 at an annual interest rate of 13%, we can use the **compound interest formula**: \[ FV = P \times (1 + r)^n \] Where: - \( FV \) = Future Value (\$1,000,000) - \( P \) = Principal Investment (\$54,955.85) - \( r \) = Annual Interest Rate (13% or 0.13) - \( n \) = Number of Years **Step 1: Plug in the known values into the formula** \[ 1,000,000 = 54,955.85 \times (1 + 0.13)^n \] **Step 2: Solve for \( (1 + r)^n \)** \[ (1 + 0.13)^n = \frac{1,000,000}{54,955.85} \approx 18.2 \] **Step 3: Take the natural logarithm (ln) of both sides to solve for \( n \)** \[ \ln\left( (1.13)^n \right) = \ln(18.2) \] \[ n \times \ln(1.13) = \ln(18.2) \] \[ n = \frac{\ln(18.2)}{\ln(1.13)} \] **Step 4: Calculate the values** \[ \ln(18.2) \approx 2.9026 \] \[ \ln(1.13) \approx 0.1222 \] \[ n \approx \frac{2.9026}{0.1222} \approx 23.75 \] **Step 5: Round to the nearest whole number** \[ n \approx 24 \text{ years} \] **Conclusion:** Jamal will need to wait approximately **24 years** to become a millionaire if he invests \$54,955.85 at an annual interest rate of 13%.