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 $16,000 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $375,000. 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 $2,150 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30?

Question:

How much Bilbo Baggins needs at retirement (30 years or 360 months from now ) so that he can have a retirement income of $16,000 per month for 25 years and leave an inheritance of $1,500,000 after he passes on at the end of the 25 years?