$($a$)$ An individual is investing in a market in which a variety of spot rates and forward contracts are available.

If at time $=0$ he invests K$1,000$ for two years, he will receive K$1,118$ at time $=2.$ Alternatively, if at time $=0$ he agrees to invest K$1,000$ at time $=1$ for two years, he will receive K$1,140$ at time $=3.$ However, if at time $=0$ he agrees to invest K$1,000$ at time $=1$ for one year, he will receive K$1,058$ at time $=2.$

$($i$)$ Calculate the following rates per annum effective, implied by this data:

$($a$)$ The one$-$year spot rate at time $=0.$

$($b$)$ The two$-$year spot rate at time $=0.$

$($c$)$ The three$-$year spot rate at time $=0.[6]$

$($ii$)$ Calculate the three$-$year par yield at time $=0$ in this market.