Suppose that you want to construct a $2-$year maturity forward loan commencing in $3$ years. The face value of each bond is $$1,000.$

a$.$ Suppose that you buy today one $3-$year maturity zero$-$coupon bond with face value $$1,000.$ How many $5-$year maturity zeros would

you have to sell to make your initial cash flow equal to zero $($specifically$,$ what must be the total face value of those $5-$year zeros$)?$

b$.$ What are the cash flows on this strategy in each year?

c$.$ What is the effective $2-$year interest rate on the effective $3-$year$-$ahead forward loan?

d$.$ Confirm that the effective $2-$year forward interest rate equals $(1+f_4)(1+f_5)-1.$ You therefore can interpret the $2-$year loan rate

as a $2-$year forward rate for the last two years. Alternatively, show that the effective $2-$year forward rate equals

$\frac{(1+y_5{)}^5}{(1+y_3{)}^3}-1$

Complete this question by entering your answers in the tabs below.

Required A

a$.$ Suppose that you buy today one $3-$year maturity zero$-$coupon bond with face value $$1,000.$ How many $5-$year maturity

zeros would you have to sell to make your initial cash flow equal to zero $($specifically$,$ what must be the total face value of

those $5-$year zeros$)?($Round your answer to $4$ decimal places.$)$

c$.$ What is the effective $2-$year interest rate on the effective $3-$year$-$ahead forward loan? $($Round your answer to $2$ decimal

places.$)$

d$.$ Confirm that the effective $2-$year forward interest rate equals $(1+f_4)(1+f_5)-1.$ You therefore can interpret the $2-$year

loan rate as a $2-$year forward rate for the last two years. Alternatively, show that the effective $2-$year forward rate equals

$($Round your answer to $2$ decimal places.$)$