Question 35 Find the final amount of money in an account if \( \$ 5,300 \) is deposited at \( 3.5 \% \) interest compounded weekly and the money is left for 6 years. The final amount is \( \$ \square \). Submit Question

To find the final amount of money in an account with compound interest, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the final amount, - \( P \) is the principal amount (the initial deposit), - \( r \) is the annual interest rate (in decimal), - \( n \) is the number of times interest is compounded per year, - \( t \) is the number of years the money is invested or borrowed. Given: - \( P = 5300 \) - \( r = 3.5\% = 0.035 \) - \( n = 52 \) (since interest is compounded weekly) - \( t = 6 \) Now, we can plug these values into the formula: \[ A = 5300 \left(1 + \frac{0.035}{52}\right)^{52 \times 6} \] First, calculate \( \frac{0.035}{52} \): \[ \frac{0.035}{52} \approx 0.0006730769 \] Now, calculate \( 52 \times 6 = 312 \). Now we can substitute these values back into the formula: \[ A = 5300 \left(1 + 0.0006730769\right)^{312} \] Calculating \( 1 + 0.0006730769 \): \[ 1 + 0.0006730769 \approx 1.0006730769 \] Now raise this to the power of 312: \[ A \approx 5300 \times (1.0006730769)^{312} \] Using a calculator to find \( (1.0006730769)^{312} \): \[ (1.0006730769)^{312} \approx 1.12749685 \] Now multiply this by 5300: \[ A \approx 5300 \times 1.12749685 \approx 5972.43 \] Thus, the final amount in the account after 6 years is approximately: \[ \boxed{5972.43} \]