1. **Problem statement:** You deposit 750 each month into a savings annuity at an annual interest rate of 3.5%. We want to find: a. The amount in the account after 25 years. b. The total money deposited. c. The total interest earned. 2. **Formula for future value of an ordinary annuity:** $$A = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $A$ is the amount in the account after $n$ periods, - $P$ is the monthly deposit, - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of deposits (months). 3. **Calculate parameters:** - Annual interest rate = 3.5% = 0.035 - Monthly interest rate $r = \frac{0.035}{12} = 0.0029167$ - Number of months $n = 25 \times 12 = 300$ - Monthly deposit $P = 750$ 4. **Calculate future value $A$:** $$A = 750 \times \frac{(1 + 0.0029167)^{300} - 1}{0.0029167}$$ Calculate $(1 + 0.0029167)^{300}$: $$ (1.0029167)^{300} \approx 2.34935 $$ So, $$A = 750 \times \frac{2.34935 - 1}{0.0029167} = 750 \times \frac{1.34935}{0.0029167} \approx 750 \times 462.63 = 346972.5$$ 5. **Total money deposited:** $$\text{Total deposits} = P \times n = 750 \times 300 = 225000$$ 6. **Total interest earned:** $$\text{Interest} = A - \text{Total deposits} = 346972.5 - 225000 = 121972.5$$ **Final answers:** - a. Amount in account after 25 years: $346972.5$ - b. Total money deposited: $225000$ - c. Total interest earned: $121972.5$