$2$ pts$)$ The following securities pay risk$-$free cash flows over the next three years:

Cash Flows

Security Price Today In $1$ Year In $2$ years In $3$ Years

B$19510000$

B$29001000$

B$38000100$

C $?200400300$

D $1,075400200600$

$($a$)$ What is the no$-$arbitrage price of security C$?$

$($b$)$ Is security D correctly priced? If so$,$ explain why. If not, demonstrate how you can

exploit the arbitrage opportunity.

$($c$)$ Determine the spot rates $($to the nearest $0\mathrm{.}01\%)$ and the discount factors for this market.