On the basis of $2001$ CSO Table of Mortality for males constructed in Tables $1$

and $2($From Assignment $4$ Q$6),$ and interest at $5\%$ per annum effective,

$($a$)$ Calculate the NSP for the following annuity policies issued to a life aged $55$:

$($i$)10-$year immediate life annuity with $$15,000$ per year for male, smoker,

$($ii$)10-$year immediate life annuity with $$15,000$ per year for male, nonsmoker.

$($b$)$ A $5-$year deferred annuity product has a NLP with premiums payable at the beginning

of each policy year in the first five years. The deferred annuity product is issued to a life

aged $55$ expecting annuity income starting from age $60$ for $5$ years. Calculate the NLP

for the following deferred annuity policies:

$($i$)5-$year deferred $5-$year life annuity with $$20,000$ per year for male, smoker,

$($ii$)5-$year deferred $5-$year life annuity with $$20,000$ per year for male, nonsmoker.