Final answer:
Using the future value of an annuity formula, we can calculate Mary's retirement annuity based on $50 monthly contributions at an 8% annual interest rate amortized over 45 years. With 540 payments and monthly compounding interest, she will have accumulated a considerable sum by age 65 for her retirement.
Step-by-step explanation:
Mary is interested in starting an annuity account for her retirement at age 65 with a monthly contribution of $50 and an annual interest rate of 8%. To calculate the future value of Mary's annuity, we use the future value of an annuity formula: FV = P × rac{((1 + r)^n - 1)}{r}, where P is the periodic payment, r is the periodic interest rate, and n is the total number of payments. Monthly, the interest rate is ⅖%, and Mary will make contributions for 45 years, which translates to 540 monthly payments.
Firstly, we convert the annual interest rate to a monthly rate: 8% annual interest rate = 0.08 annual rate = 0.08/12 per month = 0.0066667 monthly rate. Mary's periodic payment is $50. Now, substituting these values into the future value formula: FV = $50 × rac{((1 + 0.0066667)^540 - 1)}{0.0066667}. The result after calculating is a substantial amount Mary can expect for her retirement.
Thus, the power of compound interest plays a significant role in the growth of Mary's savings over time. Starting to save early, as Mary has decided, is beneficial for accumulating a sizeable retirement fund.