T
trjar
Member
Two offices in different towns of the same life insurance company write 25-year term assurance policies. Below are data from these two offices relating to policyholders of the same age. Both deaths and policies in force are on an age last birthday basis.
Gasperton Great Hawking
Policies in force on 1 January 2009 2,000 1,770
Policies in force on 1 January 2010 2,100 1,674
Deaths in calendar year 2009 25 21
(ii) Calculate the central death rate for the calendar year 2009 at this age for the offices in Gasperton and Great Hawking.
A detailed examination of the records shows that 50% of the policyholders in
Gasperton at both censuses were smokers, and 20% of policyholders in Great Hawking at both censuses were smokers. National death rates at this age for smokers in 2009 were 40% higher than those for non-smokers.
(iii) Estimate the central death rates for smokers and non-smokers in Gasperton and Great Hawking.
The first part is simple and straight.
For the second part the solution says
Rate_Gasperton = 0.5 Rate of Smokers in Gasperton + 0.5 Rate of Non-Smokers in Gasperton.
It is not clear how we get this equation.
I understand that when population is split 50-50 in smokers and non smokers the exposed to risk will be divided by a factor of 2 but we don't know the split for the deaths so how can we split the rates like in the above equation.
Any ideas ?
Thanks
Gasperton Great Hawking
Policies in force on 1 January 2009 2,000 1,770
Policies in force on 1 January 2010 2,100 1,674
Deaths in calendar year 2009 25 21
(ii) Calculate the central death rate for the calendar year 2009 at this age for the offices in Gasperton and Great Hawking.
A detailed examination of the records shows that 50% of the policyholders in
Gasperton at both censuses were smokers, and 20% of policyholders in Great Hawking at both censuses were smokers. National death rates at this age for smokers in 2009 were 40% higher than those for non-smokers.
(iii) Estimate the central death rates for smokers and non-smokers in Gasperton and Great Hawking.
The first part is simple and straight.
For the second part the solution says
Rate_Gasperton = 0.5 Rate of Smokers in Gasperton + 0.5 Rate of Non-Smokers in Gasperton.
It is not clear how we get this equation.
I understand that when population is split 50-50 in smokers and non smokers the exposed to risk will be divided by a factor of 2 but we don't know the split for the deaths so how can we split the rates like in the above equation.
Any ideas ?
Thanks