Assume that your friend is now age $53$ and plans an early retirement at age $60.$ He will be able to save $$36,000$ per year for the next three years and $$120,000$ per year for the following four years. In addition, he has $$900,000$ currently invested in undeveloped real estate.

$($a$)$ If your friend$$s annual savings over the next seven years are deposited in an account that pays $6\%$ compounded annually and the value of his real estate appreciates at the rate of $10\%$ per year, how much will he have upon retirement at age $60?($Disregard taxes.$)$

$($b$)$ Your friend expects to live to be $90--$ that is$,$ he expects to live for $30$ years after retirement. If at age $60$ he deposits all his wealth in a saving account that pays $7\%$ annual interest, how much should he withdraw at the end of each year to end up with a zero balance in the year of his expected death?

$($c$)$ Assume all the conditions in part $($b$)$ except that your friend wants to leave an estate of $$375,000$ when he dies. How much can he draw out of the account each year after he reaches age $60?$