Find the final amount of money in an account if \( \$ 2,200 \) is deposited at \( 7.5 \% \) interest compounded weekly and the money is left for 8 years. The final amount is \( \$ \) decimal places Submit Question

To find the final amount using compound interest, we can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit or investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested or borrowed for, in years. For your problem: - \( P = 2,200 \) - \( r = 0.075 \) (which is \( 7.5\% \)) - \( n = 52 \) (compounded weekly) - \( t = 8 \) Plugging in the values: \[ A = 2200 \left(1 + \frac{0.075}{52}\right)^{52 \cdot 8} \] First, calculate the inside of the parentheses: \[ 1 + \frac{0.075}{52} \approx 1 + 0.0014423 \approx 1.0014423 \] Now calculate \( 52 \cdot 8 = 416 \). Thus: \[ A \approx 2200 \times (1.0014423)^{416} \] Calculating \( (1.0014423)^{416} \): \[ (1.0014423)^{416} \approx 3.2171 \] Now multiply: \[ A \approx 2200 \times 3.2171 \approx 7077.642 \] So, the final amount is approximately: \[ A \approx 7077.64 \] The final amount is \( \$ 7,077.64 \).