A derivative security of European style with expiration in 1 year has this payoff: max(0, min(3K-S, S-K)), where K=10 is the strike price and S is the price of the underlying stock at expiration. The stock currently trades at 25, and the following prices for European options on the stock are known (all expiring in 1 year):

Type Strike Price

Call 10 16.76

Call 20 7.02

Put 10 0.85

Put 20 6.05

(a) Draw the graph of the payoff as a function of S

(b) What is the 1-year interest rate?

(c) What is the price P of the derivative security?