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Increasing Annuities

M

moreoomph

Member
Hi

I am currently trying to work out the most accurate simplification of the present value of the following cashflows:
- Annual increases of 4% happening half way through the first year and annually after that
- Monthly discounting of 0.5%

Can anyone offer any advice?
- I have tried allowing for the discounting and escalation of these annually (doesn't allow for the escalations starting at 6 months) but the answer is not very accurate (particularly for long durations)
- I have allowed for discounting and escalation monthly (again doesnt allow for the escalations starting at 6 months)
- I have tried to have an adjusted i(12) which allows for annual escalation but monthly discounting (didnt really work and no allowance for 6months!)

Can anyone think of a way to approach this using an annuity function rather than using a cashflow approach?

Thanks in advance!
 
You're on the right lines with the i(12) approach. The only thing you have to do is work out the value of the annuity from the six month point, discount that back six months, and add on the annuity for the first six months, something along the lines of

\[
\require{enclose}
a^{(12)}_{\enclose{actuarial}{0.5}}+v^{-\frac{1}{2}} \times (Ia)^{(12)}_{\enclose{actuarial}{n-0.5}}
\]

And please do bear in mind I've forgotten most of the financial maths I ever knew! In particular, I'm not sure if the fractional parts work correctly, but the general approach is what I'm getting at.
 
Calum said:
You're on the right lines with the i(12) approach. The only thing you have to do is work out the value of the annuity from the six month point, discount that back six months, and add on the annuity for the first six months, something along the lines of

\[
\require{enclose}
a^{(12)}_{\enclose{actuarial}{0.5}}+v^{-\frac{1}{2}} \times (Ia)^{(12)}_{\enclose{actuarial}{n-0.5}}
\]

And please do bear in mind I've forgotten most of the financial maths I ever knew! In particular, I'm not sure if the fractional parts work correctly, but the general approach is what I'm getting at.
Click to expand...

Would you please guide me how did you use those actuarial notations here?
 
Thanks Calum

Do you know if you can take account of the annual increases but monthly discounting?
 
I *think* \((Ia)^{(12)}\) already is increasing annually but paid monthly - have a check and see. If not, I think you'll have to add up a series of annual annuities allowing for the increase and discounting.
 
Calum said:
I *think* \((Ia)^{(12)}\) already is increasing annually but paid monthly - have a check and see. If not, I think you'll have to add up a series of annual annuities allowing for the increase and discounting.
Click to expand...

Yup that's right. Not in the UK course (but is in the US).
 
Ct1

hi, i registered for CT1 for September 2013 and i just need some one to discuss with on line
 
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