Marcus receives an inheritance of \( \$ 7,000 \). He decides to invest this money in a 13 -year certificate of deposit (CD) that pays \( 4.0 \% \) interest compounded monthly. How much money will Marcus receive when he redeems the \( C D \) at the end of the 13 years? Marcus will receive \( \$ \square \). (Round to the nearest cent.)

To calculate the amount Marcus will receive when he redeems his certificate of deposit (CD) at the end of 13 years, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money), which is \( \$ 7,000 \). - \( r \) is the annual interest rate (decimal), so \( 4.0\% = 0.04 \). - \( n \) is the number of times that interest is compounded per year (monthly, so \( n = 12 \)). - \( t \) is the time the money is invested for in years, which is 13 years. Now, plug in the values: \[ A = 7000 \left(1 + \frac{0.04}{12}\right)^{12 \times 13} \] Calculating the values step-by-step: 1. Calculate \( \frac{r}{n} \): \[ \frac{0.04}{12} \approx 0.0033333333 \] 2. Add 1 to this value: \[ 1 + 0.0033333333 \approx 1.0033333333 \] 3. Calculate \( nt = 12 \times 13 = 156 \). 4. Raise \( 1.0033333333 \) to the power of \( 156 \): \[ (1.0033333333)^{156} \approx 1.747422 \] 5. Calculate \( A \): \[ A \approx 7000 \times 1.747422 \approx 12231.95 \] Thus, rounding to the nearest cent, Marcus will receive \( \$ 12,231.95 \).