20. Jocelyne and Jacques have been saving for a "dream vacation." For 10 years, they deposited $\$ 100$ at the end of each month into an account that pays $9 \%$ interest compounded monthly. How much do they now have for their "dream vacation"?
Answer
\(\boxed{19,351.43}\) is the total amount saved for the dream vacation.
Step 1 ：Convert the annual interest rate to a monthly interest rate: \(r = \frac{0.09}{12} = 0.0075\)
Step 2 ：Calculate the total number of payments: \(n = 10 \times 12 = 120\)
Step 3 ：Use the future value of annuity formula: \(FV = P \times \frac{(1 + r)^n - 1}{r}\)
Step 4 ：Plug in the values: \(FV = 100 \times \frac{(1 + 0.0075)^{120} - 1}{0.0075}\)
Step 5 ：Calculate the future value: \(FV = 19351.42770833082\)
Step 6 ：\(\boxed{19,351.43}\) is the total amount saved for the dream vacation.
