1. **State the problem:** Zack deposits 1500 every 3 months into a savings account with an annual interest rate of 3.7% compounded quarterly. We want to find the total amount saved after 5 years. 2. **Formula used:** This is a problem of future value of an ordinary annuity compounded quarterly. The formula is: $$A = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $A$ is the amount accumulated after $n$ periods, - $P$ is the payment per period, - $r$ is the interest rate per period, - $n$ is the total number of payments. 3. **Identify values:** - $P = 1500$ - Annual interest rate = 3.7% = 0.037 - Compounded quarterly means 4 times a year, so $r = \frac{0.037}{4} = 0.00925$ - Number of years = 5, so total payments $n = 5 \times 4 = 20$ 4. **Calculate:** $$A = 1500 \times \frac{(1 + 0.00925)^{20} - 1}{0.00925}$$ 5. Calculate $(1 + 0.00925)^{20}$: $$1.00925^{20} \approx 1.197992$$ 6. Substitute back: $$A = 1500 \times \frac{1.197992 - 1}{0.00925} = 1500 \times \frac{0.197992}{0.00925}$$ 7. Simplify fraction: $$\frac{0.197992}{0.00925} \approx 21.4059$$ 8. Multiply by payment: $$A = 1500 \times 21.4059 = 32108.85$$ **Final answer:** After 5 years, Zack will have saved approximately **32108.85**.