$($a$)$ A government issues a $90-$day Treasury Bill at a simple rate of discount of $6\%$ per annum. Calculate the effective rate of return per annum received by an investor who purchases the Bill at issue and holds it to maturity. $[3]$

$($b$)$ Define the characteristics of a government index$-$linked bond. $[2]$

$($c$)$ Explain why most index$-$linked securities issued carry some inflation risk, in practice.