Company $Z$ enters into a $5-$year interest rate swap contract on $1$ January

$2015$ as the fixed$-$rate payer party. The settlement period is one year. The

settlement dates are $31$ December of each year from $2015$ to $2019.$ The spot

rates of interest at the beginning of various years for investment horizons of

$t=1,2,3,4$ and $5$ years are given in the following table.

$($a$)$ Assuming a level notional amount of $$1$ million for the contract, deter$-$

mine the swap rate.

$($b$)$ Suppose the contract is an accreting swap with notional amounts of $$1$

million, $$3$ million, $$5$ million, $$7$ million and $$9$ million. Determine

the swap rate.

$($c$)$ Suppose the contract is an amortizing swap with notional amounts of $$5$

million, $$4$ million, $$3$ million, $$2$ million and $$1$ million. Determine

the swap rate.

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