Question $4(15$ marks$)$ ABC insurance company accepts fire business up to a maximum sum

insured of $$500,000.$ To limit its maximum liability per risk to $$100,000,$ABC insurance company

is considering the following excess of loss reinsurance:

Per risk excess cover of $$400,000xS$$$100,000$ with premium adjustable at a certain

percentage $($commercial rate$)$ of gross net premium income $($GNPI$).$

This cover has one reinstatement pro rata as to the amount, payable at $25\%.$

Assume:

$(1)$ ABC insurance company's expected GNPI is $$10$ million;

$(2)$ during the treaty year, the total claim is $3$ million. Only two claims $($i$.$e$.,$ $$350,000$ and $$220,000)$

exceed the $$100,000$ deductible under the proposed risk excess of loss cover.

$4\mathrm{.}1$ The reinsurer uses a loaded burning cost method to calculate the commercial rate for the above

excess of loss cover. The aggregated GNPI and claims to cover in the past five years are $52$

million and $5\mathrm{.}85$ million, respectively. A loading factor of $\frac{100}{{75}^{th}}$ is used. Calculate the

commercial rate for the cover. $(6$ marks$)$

$4\mathrm{.}2$ What would be the total amount of claims that can be recovered from the excess of loss cover?

$(4$ marks$)$

$4\mathrm{.}3$ What would be the total reinsurance premium for the cover payable to the reinsurer by the end

of the treaty year? Keep a $2-$decimal place for your answer. $(5$ marks$)$