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in BUS 2016H - Financial Mathematics by


Why does the memo accumulate each payment within the first pattern for only one year ? I would think you would need to either put all payments to time 0 or time 4 and then count that as one group altogether . 

2 Answers

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by (240 points)

Good morning, I will have a look at the question now and get back to you with an answer.

+1 vote
by (240 points)
The total value of the four payments in the first year is R100 so X=R100 and X/4=R25. The total value of the four payments in the second year is R200 so X=R200 and X/4=R50 etc. The memo has used the annuity formula X[((1+i)^1-1)/i^(4)] where i is the effective interest rate but you would be able to use the other method using X/P and i^(4)/4 too. 

The reason that the memo is accumulating each four payment period for a year is to create a perpetuity in arrears of 4 year payments. Each year is considered as one payment and then each four year period is being considered as a "group" of payments that keeps repeating. 

Please let me know if you require any further explanation. 
by (130 points)

Hi, i understand that we are grouping the 4 payments but  what I don;t understand is why we aren't finding the value of the group at the same time point? 

For example Q4 of Tutorial 5 I answered it like this: X=100v+200v^2+300v^3=481.59 

PV= X x advanced level annuity of 33 years to get 1936.40. 

Is it different because we're working with future values? 

Thanks for the help Tarryn :)

by (240 points)

Sorry, the memo does accumulate it all to t=4 but it forgets to put the (1+0.06)^i terms into the equation for X. The first term should be multiplied by (1.06)^3, the second by (1.06)^2 and the third by (1.06). This will give you X=R868.710. If you put their equation into your calculator, you will get R817.78 and not R868.710. The rest of the solution seems to be correct. I have handwritten the correct solution but unfortunately the picture is too large to attach to this comment. If you would like to see it then please contact me on marxtarryn@gmail.com. 

by (130 points)

Ah makes sense ! Thank you.