1. **State the problem:** Ashika borrows 180000 at 4.8% per annum compounded monthly, repaid monthly over 20 years. We use the formula $$PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}$$ to find monthly repayment and balances. 2. **Find values of $i$ and $n$: ** - Annual interest rate = 4.8% = 0.048 - Monthly interest rate $$i = \frac{0.048}{12} = 0.004$$ - Number of monthly payments $$n = 20 \times 12 = 240$$ 3. **Calculate monthly repayment $PMT$: ** Rearranging formula: $$PMT = PV \times \frac{i}{1 - (1 + i)^{-n}}$$ Substitute values: $$PMT = 180000 \times \frac{0.004}{1 - (1 + 0.004)^{-240}}$$ Calculate denominator: $$(1 + 0.004)^{-240} = (1.004)^{-240} \approx 0.392838$$ So denominator: $$1 - 0.392838 = 0.607162$$ Thus: $$PMT = 180000 \times \frac{0.004}{0.607162} = 180000 \times 0.006587 = 1185.66$$ 4. **Total amount paid over 20 years: ** $$\text{Total} = PMT \times n = 1185.66 \times 240 = 284558.40$$ 5. **Total interest paid: ** $$\text{Interest} = \text{Total} - PV = 284558.40 - 180000 = 104558.40$$ 6. **Outstanding balance after 200th payment: ** Use formula for outstanding balance after $n$ payments: $$\text{Balance} = PMT \times \frac{1 - (1 + i)^{-(N-n)}}{i}$$ Where $N=240$, $n=200$: $$\text{Balance} = 1185.66 \times \frac{1 - (1.004)^{-(240-200)}}{0.004}$$ Calculate exponent: $$(1.004)^{-40} \approx 0.852143$$ Calculate numerator: $$1 - 0.852143 = 0.147857$$ Calculate balance: $$1185.66 \times \frac{0.147857}{0.004} = 1185.66 \times 36.964 = 43810.44$$ **Final answers:** - $i = 0.004$ - $n = 240$ - $PMT = 1185.66$ - Total paid = 284558.40 - Interest paid = 104558.40 - Outstanding balance after 200th payment = 43810.44