A life office issues a $3-$year without$-$profit endowment assurance policy to a man aged $62.$ The sum assured of $3,000$ is payable on maturity or at the end of the policy year of death with level annual premiums of $945$ payable throughout the term of the policy. The life office incurs initial expenses of $40$ in putting the policy on its books, renewal expenses of $10$ at the beginning of each subsequent policy year and $50$ on the payment of the sum assured. It is assumed that interest will be earned at $6\%$ per annum and mortality will be in accordance with A$1967-70($ultimate mortality$).$ Reserves are calculated on a net premium method using a rate of interest of $3\%$ per annum and mortality in accordance with A$1967-70($ultimate mortality$).$ Assuming that no surrenders or lapses occur, calculate using a profit testing analysis: $($i$)$ the profit made at the end of each of the three years provided the policy is in force at the beginning of the year, $(9$ marks$)($ii$)$ the net present value of the profit on the policy at the outset assuming a risk discount rate of $8\%$ per annum, $(6$ marks$)($iii$)$ the profit margin using a rate of interest of $6\%$ per annum. $(5$ marks$)$