Joint life notation, probabilities & contracts, ActEd Question 5: A man and a woman both aged 50 exact effect a joint life annuity of 10,000 per annum payable monthly in advance from age 65 throughout their joint lifetimes and of 5,000 per annum, also payable monthly in advance, throughout the lifetime of the survivor. Both lives must survive to age 65 for the annuity to be payable. Premiums are paid annually in advance throughout the deferred period, but cease if either life dies during the deferred period. Calculate the annual premium on the following basis: Expenses: none Mortality: PA92C20 Interest: 4% per annum My approach was to write the EPV benefits as . However, this is different from the solution as they did not use deferred annuities. Expanding the expression above also does not give the same expression as the solutions. May I know where I have gone wrong above? From my calculations, the second term in my expression is different from the solution.
Hi, Overall I like your approach here and it's a really great skill for the exam to be able to manipulate expressions in this way. However, there are two issues I can see: The first is in the switch from the deferred last survivor annuity to single life plus single life minus joint life. The last survivor annuity only comes into play if both lives survive the deferred period: "Both lives must survive to age 65 for the annuity to be payable." In setting it up as you have there is allowance for the EPV of benefits if only one life dies during the deferred period. You can see this because the two single life annuities that you are left with are contingent only on either the male being alive or female being alive in 15 years time rather than both. Secondly in the third line of the expanded benefits the monthly nature of the annuity has been dropped and that leads to there being two lots of -11/24 missing from your expression. Hope that helps. If not please feel free to come back for clarification. Joe
