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.
Last edited by a moderator: Feb 4, 2022