The prices of zero$-$coupon bonds with various maturities are given in the following table.

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.$

$\backslash$table$[[\backslash$table$[[$Maturity$],$

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

Required $A$

Required B

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.$)$

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$\backslash$table$[[,,],[$a$.,5-$year maturity zeros,$3,373\mathrm{.}8300,],[$c$.,2-$year interest rate,,$\%[($Years$)]],$Price$],[1,$$$996\mathrm{.}04$

The prices of zero$-$coupon bonds with various maturities are given in the following table.

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.$

$\backslash$table$[[\backslash$table$[[$Maturity$],[($Years$)]],$Price$],[1,$$$996\mathrm{.}04$