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+1 vote
in BUS 1003H - Introduction to Financial Risk by (330 points)

Given that \(l_{19} = 100000 \) and that \(q_x=0.000034x^2\). calculate \(l_{17}\).

I tried to use \(_{2}p_{17}\) but i got stuck where i had to compute \( \frac{l_{19}}{(1-_2q_{17})}\) because i already had a value of \(q_{17}\) not \(_2q_{17}\). it would be wrong for me to multiply \(q_{17}\) by 2 right?

1 Answer

+1 vote
by (3.1k points)

It would indeed be wrong to multiply \(q_{17}\) by \(2\). Also remember that \( _{2}{q}_{17} \neq _{1}{q}_{17} \times _{1}{q}_{18}\). Death probabilities don't work like this 'cause once you're dead, you're dead - you can't find the probability of dying at age 18 if you already died at 17!

However, you absolutely can do that with survival probabilities! So, to calculate \(l_{17}\) we need to change the death probabilities into survival probabilities and then work with those: $$_2p_{17}=p_{17} \times p_{18}=(1-q_{17}) \times (1-q_{18})$$

I leave the rest to you!