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 $$32,000$ 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 $10$ years at an estimated cost of $$420,000.$ Third, after he passes on at the end of the $25$ years of

withdrawals, he would like to leave an inheritance of $$1,350,000$ to his nephew Frodo. He can afford to save $$4,100$ 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 $30?$

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$