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 $$28,000$ per month for $15$ years, with the first payment received $30$ years and $1$ month from now. Second, he would like to purchase a cabin in Rivendell in $15$ years at an estimated cost of $$469,000.$ Third, after he passes on at the end of the $15$ 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.

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 $30?$

Multiple Choice

$$7,972\mathrm{.}08$

$$8,297\mathrm{.}47$

$$8,982\mathrm{.}51$

$$8,783\mathrm{.}23$

$$8,134\mathrm{.}77$