Question 4 (2 points) An account is opened with an initial deposit of \( \$ 2,400 \) and earns \( 3.9 \% \) interest compounded monthly. What will the account be worth in 21 years? (round to 2 decimal places) Your Answer:

To calculate the future value of the account after 21 years, you'll use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) = the amount of money accumulated after n years, including interest. - \( P \) = the principal amount (the initial deposit) = \( 2400 \) - \( r \) = annual interest rate (decimal) = \( 3.9\% = 0.039 \) - \( n \) = number of times that interest is compounded per year = \( 12 \) (monthly) - \( t \) = the number of years the money is invested = \( 21 \) Substituting the values in: \[ A = 2400 \left(1 + \frac{0.039}{12}\right)^{12 \times 21} \] Calculating this step-by-step: 1. Calculate the monthly interest rate: \[ \frac{0.039}{12} \approx 0.00325 \] 2. Calculate the total number of compounding periods: \[ 12 \times 21 = 252 \] 3. Now substitute back into the formula: \[ A = 2400 \left(1 + 0.00325\right)^{252} \] \[ A = 2400 \left(1.00325\right)^{252} \] 4. Calculate \( (1.00325)^{252} \): \[ (1.00325)^{252} \approx 2.5284 \] (rounded to four decimal places) 5. Finally, calculate \( A \): \[ A \approx 2400 \times 2.5284 \approx 6067.92 \] Rounding to two decimal places, the account will be worth approximately \( \$ 6,067.92 \).