# How do you calculate 0.25q2 using the balducci assumption?

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How do you calculate $$_{0.25}q_{2}$$ using the balducci assumption?  2012 UCT paper question 2

answered May 8 by (1,350 points)

Recall that under Baducci, $$_{1-t}q_{x+t} = (1-t). q_x$$. Now, the crux is the following:

$$_tp_x\,_{1-t}p_{x+t} = p_x \quad \implies _tq_x= 1 - \frac{p_x}{_{1-t}p_{x+t} } \stackrel{\text{(YOU SHOW)}}= \frac{t.q_x}{1 - (1-t).q_x}$$ under Balducci.

The rest should be fairly straightforward from there. Do you agree with my answer of 0.000157578?

I hope I haven't made any typos!