You plan to retire $33$ years from now. You expect that you will live $27$ years after retiring. You want to have enough money upon reaching retirement age to withdraw Rs$.1,80,000$ from the account at the beginning of each year you expect to live, and yet still have Rs$.25,00,000$ left in the account at the time of your expected death $(60$ years from now$).$ You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next $33$ years. You expect that you will be able to earn $12\%$ per year on your own deposits. However, you only expect to earn $6\%$ per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal? answer this question using compound intrest table, give proper mathematical steps and suitable cash flow diagram