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 $26,000 per month for 20 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 $368,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $600,000 to his nephew Frodo. He can afford to save $2,300 per month for the next 10 years.

Required:

If he can earn a 10 percent EAR before he retires and a 6 percent EAR after he retires, how much will he have to save each month in years 11 through 30?