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Q1.3

C

Cathy

Member
Hi guys,

I'm looking for some guidance on how to integrate something like aT-5 rather than just aT (where the T-5 is the time of the annuity, not the age). This occurs in the second way of writing the solution to Q1.3 part i).

Do you need to alter the limits of the integral to 0 to 5 (from 5 to 10) or do you adjust the integrand - eg change x to x-5. Or is it something else?

Any help would be appreciated.

Thanks

Cathy

PS - I'm struggling to format the text here. I hope you can understand what I mean!
 
Hi Cathy - I'm back on CT5 today too...

Okay, I think I know what you mean here - you mean if you were to integrate the second term of the second part of the second version of the formula in the solutions?
You'd be integrating

integral(from 5 to 10) 150 * v^5 * a-bar (t-5) * mu_t t_p_x dt


Though I was a bit confused by this solution altogether - isn't it easier to calculate

integral (from 0 to 10) rho(s) v^s s_p_x ds

(where rho is the function defined in the solution giving the rate of payment 100 or 150)
?

Louisa
 
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