Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $24,000 per month for 25 years. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $340,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1.5 million to his nephew, Frodo. He can afford to save $2,500 per month for the next 10 years.

a) If he can earn 10 % per year (monthly compounding) for his entire life, how much will he have to save each month in years 11 through 30?

Please answer all aspects in the paragraph questions and show each step involved. Please show formulas as well.