September 2009 - Q10

Hi all,

I've had a poke around the forums although I gather that the general opinion is that this question was nasty, there doesn't seem to be anything explaining my area of confusion! So I was wondering if anyone could help

I'm generally unsure what's happening with the increasing annuity section of the payments - and how they jumped to a continuous annuity (in part iii, in part ii they basically said the increasing annuity didn't need to be discounted because increase rate = discount rate).

Does anyone have any idea what's going on here please?

Thanks x

 

And also - I initially attempted to evalulate the increasing annuity in part ii using the formula (as given in the summary to chapter 7) with n = 50, i = 0.01 but this doesn't give me 50 as it should if I'm to obtain the 20 X 50 relating to this cost in the solutions.

Any ideas??

 

The net rate you need to use is 0 not 0.01, since the increase and discount are at the same rate.
consider discrete payments first (annually)
If you have a payment of 100 now which increases at 4%pa. Next year's payment is 104.
If you discount this at 4% you get 100. Same for payment in two years, etc
And you can extend this to any discount rate and continuous payments.

As a general rule the formulae go belly up when you stick i=0 in. but you just need to forget about interest/discount, number of payments times rate.

The 20x50 is 20 years of 50 each (no discounting because increase = discount rate; they cancel out)

and continuous annuity because the questions says so (continuous increases, incurred continuously)

 

This seems to cover ii, although I'm more confused about part iii...

From the wording of the question it's a continously increasing continously paid annuity and somehow they've got from that to a straight forward continously paid annuity (ignoring the continuously increasing portion??)

I would've expected to see a formula involved Ia bar (bar over both I and a) and they're using a bar...