1. **State the problem:** We want to find the quarterly payment amount deposited at the beginning of every three months to accumulate 10200 in 6 years with 6% interest compounded monthly. 2. **Identify the formula:** Since payments are made at the beginning of each period, this is an annuity due problem. The future value of an annuity due is given by: $$FV = P \times \frac{(1 + i)^n - 1}{i} \times (1 + i)$$ where $P$ is the payment per period, $i$ is the interest rate per period, and $n$ is the total number of payments. 3. **Calculate parameters:** - Annual nominal interest rate $r = 0.06$ - Compounded monthly means monthly interest rate $i_m = \frac{0.06}{12} = 0.005$ - Payments are quarterly (every 3 months), so interest rate per payment period $i = (1 + i_m)^3 - 1 = (1 + 0.005)^3 - 1$ - Number of payments $n = 6 \text{ years} \times 4 \text{ payments/year} = 24$ Calculate $i$: $$i = (1.005)^3 - 1 = 1.015075 - 1 = 0.015075$$ 4. **Plug values into the formula:** $$10200 = P \times \frac{(1 + 0.015075)^{24} - 1}{0.015075} \times (1 + 0.015075)$$ Calculate $(1 + 0.015075)^{24}$: $$ (1.015075)^{24} = 1.432364$$ Calculate numerator: $$1.432364 - 1 = 0.432364$$ Calculate fraction: $$\frac{0.432364}{0.015075} = 28.693$$ Multiply by $(1 + i)$: $$28.693 \times 1.015075 = 29.123$$ 5. **Solve for $P$:** $$10200 = P \times 29.123$$ $$P = \frac{10200}{29.123}$$ $$P = 350.349$$ 6. **Final answer:** The payment amount is approximately **350.35** per quarter.