Q$1$: For a special single premium $3-$year endowment insurance on $($x$),$ you are given:

$($i$)$ Death benefits, payable at the end of the year of death are: $b_1=4500,b_2=2000,b_3=1500.$

$($ii$)$ The maturity benefit is $1000.$

$($iii$)=0\mathrm{.}05,{}_{x+t}=0\mathrm{.}03,t0.$

Calculate the single premium using E$.$P$.$