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Ch7 exam-style question; query

T

Tim.Sullivan

Member
Hi - I'm having difficulty understanding the solution for the chapter 7 exam-style question. I've attached a scanned copy highlighting the specific part that I have the issue with.

I attempted the question myself first and thought I had it right. Where I differ is on the calculation of the interest rate j. I calculated j as (0.12-0.03)/1.03 giving 0.087379 (8.74%). Applying this gives a solution of 488,022.

In the solution in the notes, j appears to be calculated as 1.087379^5-1= 52.021%. I can't understand why.

My steps were:
1) calc the PV of the first 5 years = 77426.33
2) The PV of the 10 x 5-years increasing by 1.03 each time can be represented as:
PV= 77426.33V + 77426.33V^2(1.03) + 77426.33V^3(1.03)^2 etc
or PV = 77426.33V [1 + 1.03V + 1.03^2V^2 + 1.03^3V^3 etc
3) So this is 77426.33V * a_10 (annuity due calc) at rate j. Using the (i-e/1+e) calc I get j = (0.12-0.03 / 1.03) = 0.087379.

Since we are working in 5 year periods and the annuity due calc in step 3 effectively works in 10 x 5 year periods, why does j need to be increased by a factor of (1+j)^5?

Thank you!

Tim
 

Attachments

  • exam q.pdf
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Hi Tim

I am on Ch5 at the moment but when I am on Ch7 I will pay particular attention to your question. Hopefully, I will be able to get back to you with some explanation in the next couple of weeks if no one posts before hand.

Will get back to you soon

KrisZ
 
2)The PV of the 10 x 5-years increasing by 1.03 each time can be represented as:
PV= 77426.33V + 77426.33V^2(1.03) + 77426.33V^3(1.03)^2 etc
or PV = 77426.33V [1 + 1.03V + 1.03^2V^2 + 1.03^3V^3 etc

I can see where my representation of the PV above differs from the notes, which shows as:
PV= 77426.33(1+ 1.03^5V^5 + 1.03^10V^10 + 1.03^15V^15 etc)

So I guess it makes sense to calculate j at ^5 too, but I'd like to see the logic behind it. Can someone show me how the calc would fit into the Sum of a Geometric Progression calculation? And can anyone explain the logic for j?

Thanks

Tim
 
I can see where my representation of the PV above differs from the notes, which shows as:
PV= 77426.33(1+ 1.03^5V^5 + 1.03^10V^10 + 1.03^15V^15 etc)

So I guess it makes sense to calculate j at ^5 too, but I'd like to see the logic behind it. Can someone show me how the calc would fit into the Sum of a Geometric Progression calculation? And can anyone explain the logic for j?

Thanks

Tim

i guess its because every year we need to take into account the inflation, so for each period(5 years) we need to times it 5 times, regarding the geometric progression, if we only look at the formula in the bracket, each term(from the second of course) would be the previous one times by: 1.03^5 * v^5, applying the geometric formula would give the result, hope this helps:)
 
i guess its because every year we need to take into account the inflation, so for each period(5 years) we need to times it 5 times, regarding the geometric progression, if we only look at the formula in the bracket, each term(from the second of course) would be the previous one times by: 1.03^5 * v^5, applying the geometric formula would give the result, hope this helps:)

This, basically.

The inflation is 3% p.a., and you're working out the inflationary effects of 5 years' worth of inflation, that is, 1.03^5.
 
For the progression, if you let say w=1.03^5v5 you will get it into the usual geometric format of

1+ w + w^2......
 
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