1. **Problem Statement:** You want to retire in 30 years and need 10 lacs rupees at that time. You want to find out how much money you need to save each month if your investments earn an average annual return of 8%. 2. **Formula Used:** This is a future value of an ordinary annuity problem. The formula to find the monthly payment $P$ is: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $FV$ = future value needed = 10,00,000 rupees $r$ = monthly interest rate = $\frac{8\%}{12} = \frac{0.08}{12} = 0.0066667$ $n$ = total number of months = $30 \times 12 = 360$ 3. **Rearranging the formula to solve for $P$: $$P = \frac{FV \times r}{(1 + r)^n - 1}$$ 4. **Substitute the values:** $$P = \frac{1000000 \times 0.0066667}{(1 + 0.0066667)^{360} - 1}$$ 5. **Calculate the denominator:** $$ (1 + 0.0066667)^{360} = (1.0066667)^{360} \approx 10.9356$$ So, $$10.9356 - 1 = 9.9356$$ 6. **Calculate the numerator:** $$1000000 \times 0.0066667 = 6666.7$$ 7. **Calculate the monthly payment $P$: $$P = \frac{6666.7}{9.9356} \approx 671.1$$ **Answer:** You need to save approximately 671 rupees each month to reach 10 lacs rupees in 30 years with an 8% annual return.