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 $25,000 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 15 years at an estimated cost of $469,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $700,000 to his nephew Frodo. He can afford to save $1,600 per month for the next 15 years.
Required:
If he can earn a 9 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 16 through 30?