The force of interest, $(t),$ is a function of time and at any time $t($measure in years$)$ is given by:

$(t)=\{\begin{array}{cc}0\mathrm{.}03,& 0t10\\ at,& 1020\end{array}$

where a and $b$ are constants.

The present value of RM$100$ due at time $20$ is $50.$

$($i$)$ Calculate $a.$

The present value of RM$100$ due at time $28$ is $40.$

$($ii$)$ Calculate $b.$

$($iii$)$ Calculate the equivalent annual effective rate of discount from time $0$ to time $28.$