Betty borrow $19,800 from bank x. betty repays the loan by making 36 equal payments of principal at the end of each month. she also pays interest on the unpaid balance each month at a nominal rate of 12%, compounded monthly. immediately after the 16th payment is made, bank x sells the rights to future payments to bank y. bank y wishes to yield a nominal rate of 14%, compounded semiannually, on its investment. what price does bank x receive?

White truffles are a very prized and rare edible fungus that grow naturally in the countryside near alba, italy. suppose that it costs $200 per day to search for white truffles. on an average day, the total number of white truffles (t) found in alba is t = 20x − x 2 , where x is the number of people searching for white truffles on that day. white truffles can be sold for $100 each. if there is no regulation, how many more people will be searching for white truffles than the socially optimal number?