The force of interest per unit tim at time $t,(t),$ is given:

$(t)=\{\begin{array}{ccc}0\mathrm{.}1-0\mathrm{.}005t& \text{f}\text{o}\text{r}& t<mn\; id="EditorElement\_496481">6</mn>\\ 0\mathrm{.}07& \text{f}\text{o}\text{r}& t6\end{array}$

$($i$)$ Calculate the total accumulation at time $1$ of an investment of RM$100$ made a time $0$ and further investment of RM$50$ made at time $7.$

$($ii$)$ Calculate the present value at time $0$ of a continuous paymient strenm at the rate RMS$0$e $0\mathrm{.}05t$ per unit time received between time $12$ and time $15.$