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

Security

$1$

$2$

Market Price Today

$$980$

$$770$

Cash Flow in One Year

Weak Economy

Strong Econc

$$1,060$

$$1,060$

$$760$

$$1,030$

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

b$.$ What is the price of a security that has a payoff of $$2,200$ in the weak economy and $$2,700$ in the strong economy?

c$.$ What is the price of a security that has a payoff of $$2,600$ in the weak economy and $$3,600$ in the strong economy?

d$.$ What is the price of a security that has a payoff of $$0$ in the weak economy and $$100$ in the strong economy?

e$.$ What is the price of a security that has a payoff of $$100$ in the weak economy and $$0$ in the strong economy?

f$.$ How many units of each of the securities described in $($d$)$ and $($e$)$ would be needed to replicate the payoffs of the security described in $($b$)?$ What would be the total value of these units of the securities from $($d$)$ and $($e$)?$

g$.$ How many units of each of the securities described in $($d$)$ and $($e$)$ would be needed to replicate the payoffs of the security described in $($c$)?$ What would be the total value of these units of the securities from $($d$)$ and $($e$)?$