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Question 8 April 2009 (Booklet 6 pag 58)

S

sir_highbury

Member
Dear Madam/Sir,
could you please explain me how the value 67.3219, right term in the DTM equation,is derived?
Thanks and best regards,
SH
 
The discounted mean term is calculated by taking:
$$ DMT = \frac {\sum_{k=1}^n t_k C_{t_k} v^{t_k}} {\sum_{k=1}^n C_{t_k} v^{t_k}} $$
i.e. the sum of discounted cashflows multiplied by the time of each cashflow, divided by the sum of discounted cashflows.

The 67.3219 in the question is the top part of this equation, i.e. the sum of discounted cashflows multiplied by the time of each cashflow. This has been calculated using increasing annuities. An alternative way of working this out would be to take:
$$ v^9 [ \require{enclose}(Ia)_{\enclose{actuarial}{11}} + 9 \require{enclose}a_{\enclose{actuarial}{11}} ] $$
I hope this helps!
 
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