Hi

Why are the bounds of the annuity integrals for the 50k and 20k benefits not dependant on t? Because once you re-write the memo's answer in terms of annuity functions then it's clear that once the person gets sick, he/she gets the full benefit for 10 years (50k in the 1st year and 20k in the remaining years), regardless of when they got sick. So they can get sick at time 9 and still get 10 years worth of benefits beyond age 60. **But** the question specifies that benefits cease at age 60, so surely the term of the annuities should depend on the time (t) at which the person got sick to ensure that benefits are not paid beyond age 60?

Also, why are the bounds of the 20k annuity from 1 to 9 instead of 1 to 10, since doesn't an integral over 1-9 only cover 8 years of benefits and the maximum benefit period for the 20k payment is 9 years? (If the person gets sick right from the beginning does he not get 50k for 1 year and 20k for the remaining 9 years if he stays sick?)

Thanks