1. **Problem Statement:** Calculate the monthly interest payment on a loan of 90000 with a principal repayment of 18000 and a 2% monthly compound interest rate. 2. **Formula Used:** Compound interest formula for monthly payment is given by $$A = P \left(1 + \frac{r}{100}\right)^n$$ where $P$ is principal, $r$ is monthly interest rate, and $n$ is number of months. 3. **Step-by-step Solution:** - Principal $P = 90000$ - Monthly repayment = 18000 - Monthly interest rate $r = 2$% - Number of months $n = 18$ 4. Calculate the amount after 18 months: $$A = 90000 \times \left(1 + \frac{2}{100}\right)^{18} = 90000 \times (1.02)^{18}$$ 5. Calculate $(1.02)^{18}$: $$ (1.02)^{18} \approx 1.432364 $$ 6. Calculate total amount: $$ A = 90000 \times 1.432364 = 128912.76 $$ 7. Total interest paid: $$ \text{Interest} = A - P = 128912.76 - 90000 = 38912.76 $$ 8. Monthly interest payment: Since principal repayment is 18000 monthly, interest portion is the difference between total monthly payment and principal repayment. 9. Total monthly payment: $$ \frac{128912.76}{18} = 7161.82 $$ 10. Monthly interest payment: $$ 7161.82 - 18000 = -10838.18 $$ This negative value indicates the monthly repayment is more than the average monthly amount, so the interest portion is calculated differently. 11. Alternatively, calculate interest for first month: $$ \text{Interest}_1 = 90000 \times 0.02 = 1800 $$ 12. So, monthly interest payment is approximately 1800 for the first month, decreasing as principal reduces. **Final Answer:** The monthly interest payment starts at approximately 1800 and decreases over time with principal repayment.