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 $$24,000$ per month for $15$ years, with the first payment received $30$ years and $1$ month from now. Second, he would like to purchase a cabin in Rivendell in $20$ years at an estimated cost of $$1,035,000.$ Third, after he passes on at the end of the $15$ years of withdrawals, he would like to leave an inheritance of $$550,000$ to his nephew Frodo. He can afford to save $$1,600$ per month for the next $20$ years.

If he can earn a $11$ percent EAR before he retires and a $8$ percent EAR after he retires, how much will he have to save each month in Years $21$ through $30?$

Multiple Choice

$$11,286\mathrm{.}89$

$$9,653\mathrm{.}96$

$$9275\mathrm{.}37$

$$11,724\mathrm{.}06$

$$9,464\mathrm{.}66$