Hello, please can someone explain the breakdown of the assurance function in the solution. If the term assurance has a benefit of 70,000 and (IA) 10,000, shouldn't the age and the tenor for (IA) be 60:5?? 2. Please also explain why there was a subtraction of 10,000 when calculating the DSAR .
(1) We need the reserve at the end of year 4, which is exactly 4 years since the start of the contract. So, at that time, the age of the policyholder is 59. The payment represents the return of unpaid annual annuity payments of 10000 a year for the remainder of the term. By the end of year 4, four payments have been made (at the end of each of years 1-4 inclusive). So there are 6 payments left (and so the term of the assurances must be 6). So, the death benefit needs to be 60,000 if they died in the next (5th) year, 50,000 if died in the 6th year, and so on, reducing to just 10,000 if they died in the last year. Now the (IA) function values a benefit of 10,000 in the 5th year, 20,000 in the 6th year, and so on, and so we need a level 70,000 assurance minus the 10,000(IA) to produce the correct benefit. (2) The death strain at risk is always: {sum assured paid on death (at end of year of death)} minus {any payment made on survival at the end of the year} minus {reserve at the end of the year} The 10,000 is the amount paid on survival at the end of the year. To explain this, the DSAR is the amount that is "at risk" from dying. This is why any death benefit sum assured is a positive amount in the DSAR, because the company will be worse off by this amount if the person dies during the year. When we have an annuity payment at the end of the year, then if the person dies during the year, then the insurance company will BETTER off by this amount. And so an end-of-year annuity payment is counted as a negative amount in the DSAR.
