financial maths-grrr! (1 Viewer)

[enveloped]

Hey sorry but nobody replied to this question so I had to make it a new post.
I found this in the Cambridge book and was a bit confused...
A finance company has agreed to pay a retired couple a pension of $15 000 per year for the next twnety years, indexed to inflation which is 3.5%.
How much will the company have paid the couple at the end of twenty years?
Immediately after the tenth annual pension payment is made, the finance company increases the indexed rate of 4% per annum to match thte increased inflation rate. Given these new conditions, how much will the company have paid the couple at the end of twenty years?

The answers are $424 195.23 and $431 235.13.
Please explain the steps! Thank you=]
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[totallybord]

OMG I was doing this as well!!
for a) I used n=20, why did you use n=9?
for b) why is it n=9 and then n=10 because they don't add up to 20...=S

 

[kooliskool]

This question is pretty tricky, if you draw the time line, it would be clearer.

a) So, it goes as like this:

At time 1 (which is one year from now), the pension pays $15000 straight away.
At time 2, the pension increases according to the inflation index, which is going to be $15000(1.035)
...
...
At time 20, this is the last pension payment, it is going to be $15000(1.035)^19, as it only inflated for 19 years.

So altogether:



b) This is even more trickier, so it goes as:

At time 1 (which is one year from now), the pension pays $15000 straight away.
At time 2, the pension increases according to the inflation index, which is going to be $15000(1.035)
...
At time 10, the pension is going to be 15000(1.035)^9, (note that it only inflated for 9 times since time 1, not 10 times)
At time 11, it says immediately after last payment, which is the tenth one, it changed its inflation rate, so it's going to be 15000*(1.035)^9*1.04
At time 12, it continues to inflate at 4% per annum, so it's going to be 15000*(1.035)^9*1.04^2
...
At time 20, this is the last pension payment, it is going to be $15000*(1.035)^9*1.04*10 (note that this is the tenth time it inflates with 4% per annum, not the 9th time.

So it's:





Hope this helps, and feel free to ask me anything you don't understand