1. **Problem statement:** We need to find two equal payments that will settle a debt of 8149 dollars. The payments are due in 1 month and 8 months, and the interest rate is 5% compounded monthly. The focal date is today. 2. **Formula and explanation:** The present value (PV) of each payment is calculated using the formula for compound interest: $$PV = \frac{P}{(1 + i)^n}$$ where $P$ is the payment amount, $i$ is the monthly interest rate, and $n$ is the number of months until the payment. 3. **Calculate the monthly interest rate:** $$i = \frac{5\%}{12} = \frac{0.05}{12} = 0.0041667$$ 4. **Set up the equation for the total present value of the two payments:** $$8149 = \frac{P}{(1 + 0.0041667)^1} + \frac{P}{(1 + 0.0041667)^8}$$ 5. **Calculate the discount factors:** $$\frac{1}{(1 + 0.0041667)^1} = \frac{1}{1.0041667} \approx 0.99585$$ $$\frac{1}{(1 + 0.0041667)^8} = \frac{1}{1.034} \approx 0.96621$$ 6. **Sum the discount factors:** $$0.99585 + 0.96621 = 1.96206$$ 7. **Solve for $P$:** $$8149 = P \times 1.96206$$ $$P = \frac{8149}{1.96206} \approx 4154.5$$ 8. **Round to the nearest dollar:** $$P \approx 4155$$ **Final answer:** Each payment should be 4155 dollars.