A man borrows $500,000 at 15% interest compounded quarterly.

(a) Suppose he intends to pay the entire amount (principal and all interest) in one lump sum at the end of 25 years. He intends do this by making quarterly deposits at the end of each quarter into a sinking fund that pays 14% compounded quarterly. Find the necessary quarterly payment into the sinking fund.

(b) Suppose he makes quarterly payments which begin with $20,000 at the end of the first quarter, and increase by $100 every quarter thereafter. Find the outstanding balance immediately after the payment at the end of 10 years.

(c) Suppose he makes quarterly payments which begin with $20,000 at the end of the first quarter, and decrease by 2% every quarter thereafter. Find the outstanding balance immediately after the payment at the end of 10 years.

(d) Suppose he sets up regular quarterly payments to amortize the loan in 25 years. At exactly 10 years, he pays triple the regular payment, and then continues with theoriginal regular quarterly payments. Find the outstanding balance immediately after the payment at exactly 15 years.