As part of a pricing exercise for a Commercial Property Risk XL programme incepting on 1 January 2016 and written on a losses occurring basis, you have to calculate the earned premium for a number of policy years and compare it to the claims experience. The underlying policies of the reinsured are all annual and incept on one of these four dates: 1 January, 1 April, 1 July or 1 October. The amount written for each of these dates is specified in the table below. The table also shows the year-onyear rate changes. You can assume that across-the-portfolio rate changes are only made at 1/1 renewals.

a. Calculate the earned premium for the 2012 accident year assuming a uniform risk intensity (earning pattern) for all policies

b. Carry out the same calculation assuming that risk is distributed roughly as follows: 19% from January to March; 20% from April to June; 33% from July to September; 28% from October to December.