Below is an annual credit table for bonds from companies in the nation of Fuego. It describes the probabilities of a bond being in each of the three grades in a year.

Investment	Speculative	Junk
0.80	0.15	0.05

a) Tara currently holds a bond issued by Future Industries, a company in Fuego. Calculate the probability that her bond will NOT be junk-grade within the next 5 years. [4 marks]

b) Calculate the probability that Taras bond will NOT be speculative-grade in next two years. [3 marks]

c) Kat has just bought a strange derivative product. The payoff from this product is based on what happens to Future Industries bonds. This derivative product matures in 1 year. The table below shows the payoffs from this derivative based on each of the three possible states of the bond in 1 year:

State	Derivative Payoff
Investment	$0
Speculative	$3
Junk	$10

Assuming that Kat will hold this derivative until maturity, calculate the expected payoff from this derivative at maturity. Note that you do NOT need to discount this back to today. [3 marks