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A(t,0) and v(t,0)

Y

~yoyo~

Member
What exactly are A(t,0) and v(t,0)? How do I know which one to use? I can't find a definition in the notes... from what i can see online, A refers to an assurance/annuity and v to the present value of an income stream...but i'm not confident that this is right.

Can anyone pls clear this up for me??

Thanks! :)

yoyo
 
The capital A symbol means EPV of an assurance, but in CT1 it is the accumulation of an ammount between two times. Eg. A(t1,t2) at i% would be (1+i)^t2 / (1+i)^t1. A(t,0) would actually mean discount though because t2<t1. So A(t,0) is actually equal to v^t. I have not encountered the v notation anywhere before but i'd assume it means the same thing so v(t1,t2) would mean discount applied from t2 back to t1 and if t2<t1 it would actually mean accumulation.
 
Hi yoyo,

A stands for accumulation, so A(a,b) is the accumulated value of 1 over the time from a to b, ie. A(a,b) = (1+i)^(b-a). In your example did you mean to put A(t,0)? it's unusual to have a>b but it would just mean the discounted value of 1 paid at t at time 0, ie. v^t.

v(a,b) = A(b,a) = 1/A(a,b) is the discounted value of 1 paid at time a at time b.

Hope this helps?

*edit - looks like we posted at at the same time Devon!
 
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thanks guys!! much appreciated. makes perfect sense now. :D

and ggrzz...just to answer your question... in the solution for Q&A Bank Part 1, question 1.26, they write "A(t,0)" meaning discounting from time t to time 0. This is what confused me! I didn't know why they chose to use A(), when in other questions they had used v(). So after reading both your explanations, it seems either v() or A() can be used correctly. In this case, they could have written "v(0,t)" instead.

thanks again! happy study :)

yoyo
 
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