Hi, I saw that before but it still doesn't really answer my question as I'm still confused, so I was hoping for an explanation from a tutor.
For example, how does the memo's answer account for this statement, since the duration of the annuities are not dependant on t (time the life gets sick):
"E.g. if you get sick in the second year you will receive 50000 for one year and then you will have a maximum of 7 years to receive 20000 if you stay sick until the end of the term."
If you had to rewrite the memo's answer in terms of annuity functions as I did above, if the life gets sick in the second year they will still receive 20000 for the maximum duration as the term of the annuity is fixed. I understand that the annuity bounds are used as a 'count', but surely the maximum count should depend on t, since the benefits cease at age 60?
Also, why are the bounds of the integral relating to the 20k annuity not 1-10 (covering 9 years of benefits) instead of 1-9 (covering 8 years of benefits)?
“…..split up into the first year of being sick (0-1) and then the rest of the time being sick which is 1-9 since if the term of the policy is 10 years and you have to be sick at least 1 year to get the reduced annuity, then there are 9 possible years left to receive this given that you got sick at the start. “