1. **State the problem:** Mara started depositing 1200 per year at age 23 and made deposits for 10 years. After that, she stopped depositing but left the money to grow for 42 more years at 6% annual interest. We want to find how much money Mara has at age 75. 2. **Identify the formula:** We use the future value of an annuity formula for the deposits period and then compound the total for the remaining years. The future value of an annuity formula is: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $P$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of payments. 3. **Calculate the value at the end of the deposit period (age 33):** - $P = 1200$ - $r = 0.06$ - $n = 10$ $$FV_{10} = 1200 \times \frac{(1 + 0.06)^{10} - 1}{0.06}$$ Calculate: $$ (1.06)^{10} = 1.790847$$ $$FV_{10} = 1200 \times \frac{1.790847 - 1}{0.06} = 1200 \times \frac{0.790847}{0.06} = 1200 \times 13.18078 = 15816.94$$ 4. **Compound this amount for the next 42 years without additional deposits:** $$FV_{52} = FV_{10} \times (1 + r)^{42} = 15816.94 \times (1.06)^{42}$$ Calculate: $$ (1.06)^{42} = 10.2857$$ $$FV_{52} = 15816.94 \times 10.2857 = 162592.44$$ 5. **Final answer:** At age 75, Mara has approximately $162592.44 in her account. This calculation assumes annual compounding and deposits made at the end of each year.