$16.$ 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 $$33,500$ per month for $20$ years, with the first payment received $30$ years and $1$ month from now. Second, he would like to purchase a cabin in Rivendell in $10$ years at an estimated cost of $$415,000.$ Third, after he passes on at the end of the $20$ years of withdrawals, he would like to leave an inheritance of $$775,000$ to his nephew Frodo. He can afford to save $$4,000$ per month for the next $10$ years. If he can earn an APR of $10$ percent before he retires and an APR of $7$ percent after he retires, how much will he have to save each month in Years $11$ through $30?$

If posible I would like to know how to do this problem using the BAII plus Texas Calculator.