1. **Problem statement:** A man owes 1100 due in 2 months and 4000 due in 8 months. Creditors agree to settle by two equal payments at 4 months and 10 months. Interest rate is 6% per annum. Find the size of each payment using 4 months as the focal date. 2. **Formula and rules:** We use the formula for compound interest to bring all amounts to the focal date (4 months). The formula for amount at focal date is: $$ A = P(1 + i)^n $$ where $P$ is principal, $i$ is interest rate per period, and $n$ is number of periods. 3. **Convert all debts to focal date (4 months):** - RM1100 due in 2 months is 2 months before focal date, so we discount it forward 2 months: $$ 1100 \times (1 + i)^2 $$ - RM4000 due in 8 months is 4 months after focal date, so we discount it back 4 months: $$ 4000 \times (1 + i)^{-4} $$ 4. **Calculate interest rate per month:** Annual rate = 6% = 0.06 per year Monthly rate $i = \frac{0.06}{12} = 0.005$ 5. **Calculate amounts at focal date:** - For RM1100 due in 2 months: $$ 1100 \times (1 + 0.005)^2 = 1100 \times 1.010025 = 1111.03 $$ - For RM4000 due in 8 months: $$ 4000 \times (1 + 0.005)^{-4} = 4000 \times (1.005)^{-4} = 4000 \times 0.980296 = 3921.18 $$ 6. **Total amount at focal date:** $$ 1111.03 + 3921.18 = 5032.21 $$ 7. **Let each payment be $x$ at 4 months and 10 months. Bring both payments to focal date (4 months):** - Payment at 4 months is at focal date, so value is $x$ - Payment at 10 months is 6 months after focal date, so discount back 6 months: $$ x \times (1 + 0.005)^{-6} = x \times 0.970445 $$ 8. **Sum of payments at focal date equals total debt at focal date:** $$ x + x \times 0.970445 = 5032.21 $$ $$ x(1 + 0.970445) = 5032.21 $$ $$ x \times 1.970445 = 5032.21 $$ 9. **Solve for $x$:** $$ x = \frac{5032.21}{1.970445} = 2554.88 $$ **Final answer:** Each payment is RM2554.88.