An insurance company calculates its UPR using an individual, policy by policy approach. Calculate the UPR as at 31 December 2018 for the following annual policies: (b) Premium £3,500. Commission 10%. Started 1 July 2018. Risk starts at zero and increases daily by a constant linear amount over the policy year. Can someone explain how to solve this ? solution given - £2,362.50 (75% of risk is outstanding at year-end, so the UPR is 75% of 90% of £3,500. Did not understand how 0.75 came ?

Hi Pooja This is also in the SP7 notes - see https://www.acted.co.uk/forums/index.php?threads/sp7-upr-question-on-page-13-of-notes.16390/ The risk is increasing constantly. If you draw a picture of the risk, you should find that you get a triangle and 75% of the area of the triangle is beyond the valuation date. Or use the 'monthly' method as per the above thread. Ian

The book Pricing in General Insurance has an example spreadsheet with earned premium calculations if you want to see an alternative presentation.