1. **State the problem:** A debtor owes RM5,000 due in 2 years and RM15,000 due in 5 years. They want to pay off both debts with two equal payments: one at the end of year 1 and another at the end of year 3. The interest rate is 4% compounded monthly. We need to find the amount of each payment. 2. **Formula and important rules:** The monthly interest rate is $i = \frac{4\%}{12} = 0.0033333$ per month. The present value (PV) of a future payment $F$ due in $n$ months is: $$PV = \frac{F}{(1+i)^n}$$ We will discount all debts and payments to a common time (e.g., time 0) to equate their present values. 3. **Convert years to months:** - Debt 1: 2 years = 24 months - Debt 2: 5 years = 60 months - Payment 1: 1 year = 12 months - Payment 2: 3 years = 36 months 4. **Calculate present value of debts at time 0:** - Debt 1 PV: $$\frac{5000}{(1+0.0033333)^{24}}$$ - Debt 2 PV: $$\frac{15000}{(1+0.0033333)^{60}}$$ Calculate each: $$PV_1 = \frac{5000}{(1.0033333)^{24}} = \frac{5000}{1.083} \approx 4617.58$$ $$PV_2 = \frac{15000}{(1.0033333)^{60}} = \frac{15000}{1.2214} \approx 12275.44$$ Total PV of debts: $$4617.58 + 12275.44 = 16893.02$$ 5. **Calculate present value of payments at time 0:** Let each payment be $P$. Payment 1 at 12 months: $$PV_{P1} = \frac{P}{(1.0033333)^{12}} = \frac{P}{1.041}$$ Payment 2 at 36 months: $$PV_{P2} = \frac{P}{(1.0033333)^{36}} = \frac{P}{1.1275}$$ Total PV of payments: $$PV_{payments} = \frac{P}{1.041} + \frac{P}{1.1275} = P\left(\frac{1}{1.041} + \frac{1}{1.1275}\right) = P(0.9606 + 0.8865) = 1.8471P$$ 6. **Equate total PV of debts and payments:** $$16893.02 = 1.8471P$$ 7. **Solve for $P$:** $$P = \frac{16893.02}{1.8471} \approx 9143.44$$ **Final answer:** Each payment should be approximately RM9143.44 to settle the debts under the given conditions.