Exercise $7\mathrm{.}8$ You are given the following extract from a select life table with

four$-$year select period. A select individual aged $41$ purchased a three$-$year term

insurance with a sum insured of $$200000,$ with premiums payable annually

throughout the term.

Assume an effective rate of interest of $6\%$ per year, and no expenses.

$($a$)$ Show that the premium for the term insurance is $P=$$$323\mathrm{.}59.$

$($b$)$ Calculate the mean and standard deviation of the present value of future

loss random variable, $L_1,$ for the term insurance.

$($c$)$ Calculate the sum insured for a three$-$year endowment insurance for a

select life age $41,$ with the same premium as for the term insurance,

$P=$$$323\mathrm{.}59.$

$($d$)$ Calculate the mean and standard deviation of the present value of future

loss random variable, $L_1,$ for the endowment insurance.

$($e$)$ Comment on the differences between the values for the term insurance and

the endowment insurance.