VCE General & Further Maths Question Thread!

[vox nihili]

Could someone predict my study score?
Sacs: 87% (defs not rank one)
Exam one: 40/40
Exam two:58/60

Please post study score predictions in the study score question thread—this is for questions about Further content

[marangutan]

A principal value of $10 000 is invested in an account earning compound interest at the rate of 9% per annum. The rule for the value of the investment after n years is shown as V_n = 1.09ⁿ * 10 000

Find the amount of interest earned in the fourth year, correct to the nearest cent

[S200]

could you just sub in 3 and 4 as \(n\) and then minus the \(V_3\) from the \(V_4\)?

the difference should be the interest?

[marangutan]

could you just sub in 3 and 4 as \(n\) and then minus the \(V_3\) from the \(V_4\)?

the difference should be the interest?

Thanks, but why is V₃ involved?

[PhoenixxFire]

Thanks, but why is V₃ involved?

The question only wants the interest in the fourth year not the total interest so you have to subtract the total interest earned in the first 3 years (v3) from the total interest earned in the first four years (v4) to get just the interest in the fourth year.

[marangutan]

Q: The Central Australia tour visits Kakadu National Park where the students are shown a flock of the endangered lesser yellow-breasted scrub thrushes.  The Park Ranger leading the tour explains that there are only 2 500 birds remaining.  The Ranger tells the students that out of each 100 adult birds, only 5 chicks are raised each year.  However, on average, 500 birds die each year.

I wrote that the recurrence relation is V₀ = 2500 , V_n+1 = V_n  - 500 , however I don't know how to add in the 100 adult birds and 5 chicks raised (or if it is even necessary to add it in)

[PhoenixxFire]

Q: The Central Australia tour visits Kakadu National Park where the students are shown a flock of the endangered lesser yellow-breasted scrub thrushes.  The Park Ranger leading the tour explains that there are only 2 500 birds remaining.  The Ranger tells the students that out of each 100 adult birds, only 5 chicks are raised each year.  However, on average, 500 birds die each year.

I wrote that the recurrence relation is V₀ = 2500 , V_n+1 = V_n  - 500 , however I don't know how to add in the 100 adult birds and 5 chicks raised (or if it is even necessary to add it in)

Yep it's necessary to add it in. 5 chicks per 100 birds is 5% so the recurrence relation would be V_n+1 = 1.05V_n - 500

It could potentially be a bit different depending on if the 5 chicks are added before or after the 500 die but I'm pretty sure it would be this way around.

[marangutan]

Yep it's necessary to add it in. 5 chicks per 100 birds is 5% so the recurrence relation would be V_n+1 = 1.05V_n - 500

It could potentially be a bit different depending on if the 5 chicks are added before or after the 500 die but I'm pretty sure it would be this way around.

oh so it's like compound interest right ?
I can see what you've done, but I can't connected the dots. Can u please clarify what the 'compound factor' means for 'R' (in Vn=R^n * V0) ?

[PhoenixxFire]

oh so it's like compound interest right ?
I can see what you've done, but I can't connected the dots. Can u please clarify what the 'compound factor' means for 'R' (in Vn=R^n * V0) ?

Yeah sort of, you can't change this equation into Vn=R^n * V0 format because of the -500. You just have to leave it as V_n+1 = 1.05V_n - 500.

If you didn't have the -500 part of it then it would be Vn=1.05^n * 2500

But you can't do that because you have to -500 each equation.

[dream chaser]

Hi Guys,

Can someone please explain how to do part (c). Question is in the attachment.

Thanks

[Aaron]

Hi Guys,

Can someone please explain how to do part (c). Question is in the attachment.

Thanks

What is your current understanding of the question? Provide us with something to work with. Giving you the answer will not assist with your understanding. Why not have a go at it yourself and post how you think it can be done here. That way, we can not only give you the answer, but can address your misconceptions so that when you are given a different question like this in the future, you can be aware of the mistakes and rectify them.

In a situation like this, your incorrect working out / answer is actually a good thing because it will address the issues directly.

Once you've had a go, open spoiler

A "recurrence relation model" is essentially the same as what you see in the original question. Except instead of the 2500, -400 etc, you will use 1800 as the V0 value (as V0 represents the initial price/cost) and Vn+1 = Vn (original/prev. value) - 350 (depreciates 350 per year, which is why we use negative 350 instead of positive 350).

So the model:
V0 = 1800, Vn+1 = Vn - 350

Cheers.

[dream chaser]

Thanks Aaron. I get it how to do it now.

[dream chaser]

Hi Guys,

Need help to do this question. It is about compound interest. Specifically, Modelling compound interest with recurrence relations. Thanks

I don't know how they got an R value of 1.005. The R value I obtained was 1.00375. Has it got to do with a rounding error. When are we meant to round our answers? In the final answer, when we convert the yearly rate to a monthly rate or when we find the R value.

The question and the answer in the book are in the attachments

All help will be appreciated. Thanks

[galaxy21]

Hi Guys,

Need help to do this question. It is about compound interest. Specifically, Modelling compound interest with recurrence relations. Thanks

I don't know how they got an R value of 1.005. The R value I obtained was 1.00375. Has it got to do with a rounding error. When are we meant to round our answers? In the final answer, when we convert the yearly rate to a monthly rate or when we find the R value.

The question and the answer in the book are in the attachments

All help will be appreciated. Thanks

As the interest is compounding monthly, you need to divide 6(the monthly interest rate)/12(the number of months in 1 year)=0.5 %. Then you need to divide the 0.5 by 100 to have it as a decimal form of the percentage, and add this to 1, resulting in 1.005.
In other words, 1+(6/(100*12)=1.005.

Hope this makes some sense. How did you work it out?

[lacitam]

You divide the percentage interest by 12 because it's monthly, not annually.
Can you tell me your steps on how you got 1.00375? Not following where this came from. I'll explain where you stuffed up on.