Calculating Annuity Values

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $31,000 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 $390,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $900,000 to his nephew Frodo. He can afford to save $3,500 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Monthly savings $