Chapter 27(interpreting accounts) SP7

Discussion in 'SP7' started by Rishita Agarwal, Jan 17, 2024.

  1. Rishita Agarwal

    Rishita Agarwal Member

    Ques 27.3 -(i)
    A general insurance company has a solvency ratio of 50% of gross written premiums. Calculate this ratio at the end of the financial year assuming that:
    • the company pays no tax or dividends
    • investment income on free reserves is earned at 5% per annum
    • the reserves are exactly correct to meet claim payments
    • business is sold with an insurance profit of 3% of earned premiums
    • new business has increased by 15% over the previous year.
    query-How to calculate earned premium? (it is given 1.075 of written premium in answer)

    Ques 27.8- query

    Can someone please explain the below premium calculation-

    The constant business volumes and constant 5% increase in premiums means than written premium has increased by 5% each year. Earned premium = 1,800 / 2 + 1,800 / 1.05 / 2 = 1,757.14
     
    Rishita Agarwal, Jan 17, 2024
    #1
  2. Ian Senator

    Ian Senator ActEd Tutor Staff Member

    Both of these queries are very simple examples of the concept of premiums being earned out across two accounting periods. I suggest you revisit Chapter 15 pages 67-70 where there are lots of examples, so that you understand more complex scenarios in other questions later on...
     
    Ian Senator, Jan 18, 2024
    #2
  3. Rishita Agarwal

    Rishita Agarwal Member

    Thank you! I got the solution. Let me explain , Please correct me if I am wrong somewhere.
    • Since the assumption is that premiums are earned evenly, an additional 50% of the remaining premiums are considered earned in the second half of the year.
      50% * 0.15 = 0.075
     
    Last edited: Jan 19, 2024
    Rishita Agarwal, Jan 19, 2024
    #3
  4. Darren Michaels

    Darren Michaels ActEd Tutor Staff Member

    With the three standard assumptions of:
    • annual policies
    • policies written evenly over the year
    • risk being uniform over the policy period
    then that means half of the premium written in a given year is earned in that year and the other half is earned in the following year.

    So in this question the premiums earned in the year in question are therefore 0.5*WP(0)+0.5*1.15*WP(0)=1.075WP(0)
     
    Darren Michaels, Jan 22, 2024
    #4

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