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September 2000, Question 4 - Geometric progression?

S

stylz

Member
Hi All,

I am thinking we could do a geometric progression for the continuously paid amounts in this question with the first amount ('a' in the GP formula) being 25,000a-bar 1 (a continuous annuity of 25,000 for one year). The rest of the GP would read (1 - (1.06v)^25)/(1-1.06v). i.e the common ratio is 1.06v. This GP comes out at 21. 64 which is not that close to the 22.28 in the answer, and then when multiplied by 25,000 the difference becomes quite large so my answer ends up very different.
I'm not sure if I have explained this very well, but basically I'd like to know if you think I am on the right track in being able to use a GP instead of working out a new interest rate j (which was 1.07/1.06) for the continuous annuity. And if so, is there something I have missed since my answer does not come out the same as theirs.
Cheers
 
stylz said:
Hi All,

I am thinking we could do a geometric progression for the continuously paid amounts in this question with the first amount ('a' in the GP formula) being 25,000a-bar 1 (a continuous annuity of 25,000 for one year). The rest of the GP would read (1 - (1.06v)^25)/(1-1.06v). i.e the common ratio is 1.06v. This GP comes out at 21. 64 which is not that close to the 22.28 in the answer, and then when multiplied by 25,000 the difference becomes quite large so my answer ends up very different.
I'm not sure if I have explained this very well, but basically I'd like to know if you think I am on the right track in being able to use a GP instead of working out a new interest rate j (which was 1.07/1.06) for the continuous annuity. And if so, is there something I have missed since my answer does not come out the same as theirs.
Cheers
Click to expand...

Your method would work if it was a stepped, ie continuous level £25,000 the first year, then continuous level £25,000(1.06) the next year and so on. However, this question actually has the rate of payment increasing continuously at 6% pa.

This kind of question is pretty rare (if my memory serves me correct there's been only 2 or 3 in the last 10 years) and requires either an integral approach or a clever annuity trick.
 
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