We know the prices and payoffs for securities $1$ and $2$ and they are represented as follows:

Cash Flow in One Year

a$.$ What is the risk$-$free interest rate?

b$.$ Consider a risk$-$free security that has a payoff in one year of $$2,750.$

i$.$ How many units of each of securities $1$ and $2$ would be needed to replicate this risk$-$free

security?

ii$.$ Based on part b$.$i$),$ what is the market price today of this risk$-$free security?

iii. Based on part a$),$ what is the market price today of this risk$-$free security?

c$.$ Consider a security that has a Davoff in one vear of $$2\mathrm{.}750$ if the economv is weak and $$5\mathrm{.}500$ if the economv is strona.

a$.$ What is the risk$-$free interest rate? $($Round to four decimal places.$)$

The risk$-$free interest rate is

$\%.$