Question $2$ A life insurance office offers a without profit endowment assurance to

male lives aged $56$ exact. The sum assured is Kenya Shillings $21,500$ payable on

maturity or at the ond of the year of douth if earlier. Premiums of Keaya Shillings

$5,000$ are payable ansually in advance for the durabon of the policy. The company

holds aet premium reserves for these policies, calculated at AM$92$ Ultimate mor$-$

tality and interest of $4\%$ per annum. Sarrenders occar only the the end of the year

immediately befoce a premium is paid. The surrender value is $70\%$ of the net pre$-$

miam reserve calculated at the time the surtender value is payable. The company

uses the following assuraptinns to carry out profit tests for this contract:

Interest rate on castflows; $4\%$ per annum

Mortality: AM$92$ Select

Surrenders: $10\%$ of all policies still in force at the end of ench first, second and

third policy years

Initsil Expethse: Ketya Shalling $600$

Renewal Expense: Kenya Shilling $45$ per anmum an the second and subsecraent

premium dates.

Risk discount: $6\%$ per annom

Calculate the expected protit margin for this contract