VCE General & Further Maths Question Thread!

[clarke54321]

Hi all,

I have my recursion and finance SAC coming up this week and just have a question.

When finding the rate for compound interest loans and investments the model is 1+ r/100, whilst the model for reducing balance depreciation is 1-r/100. Could someone please explain the significance of the 1.

Thanks

[Aaron]

Hi all,

I have my recursion and finance SAC coming up this week and just have a question.

When finding the rate for compound interest loans and investments the model is 1+ r/100, whilst the model for reducing balance depreciation is 1-r/100. Could someone please explain the significance of the 1.

Thanks

My interpretation of '1' is simply the 'original' amount (1 = 100% = the original or principal amount).

Take into consideration the brackets (1 + r)

If the interest rate is 5%, then its 1 + (5/100) which is 1.05, MEANING the original amount (100%) plus an additional 5% = 105% = 1.05. Then of course, 1.05 is multiplied by itself however many periods/years.

[clarke54321]

My interpretation of '1' is simply the 'original' amount (1 = 100% = the original or principal amount).

Take into consideration the brackets (1 + r)

If the interest rate is 5%, then its 1 + (5/100) which is 1.05, MEANING the original amount (100%) plus an additional 5% = 105% = 1.05. Then of course, 1.05 is multiplied by itself however many periods/years.

Thanks Aaron 

[Coffee]

Guys, how do I go about doing this one?

Ali invested $26,000 into an account earning compound interest at the rate of 4.5% per annum. After 5 compounding periods, the value of Ali's investment will be $26,614.86 correct to the nearest cent.
The annual interest rate is compounding

A) weekly
B) fortnightly
C) monthly
D) quarterly
E) annually

Definitely missing something simple here. The answer is A but I keep getting something completely different.

[ayesha2011t]

Guys, how do I go about doing this one?

Definitely missing something simple here. The answer is A but I keep getting something completely different.

I think there's a typo in this question. I tried everything

My first method I used was [26000*(1+4.5/100*n)^5=26614.86] n=9.6
This has to be the right answer but bc you said its weekly the actual answer should be 52.

I then wanted to see if the question was actually correct. So I used 52 as my n

[26000*(1+4.5/100*52)^5] for this I got the answer 26112.69 which wasn't the amount mentioned in the question.

So I think the question is written wrong, or I made a mistake.
Guys, If I did anything wrong in my working out, pls let me know

[ayesha2011t]

Guys what does 'equal bin width' mean on the CAS? And when would I need to utilise the function?

[knightrider]

For this question attached i have a query.

i got the equation as Vn=(0.918)^n x Vo

now we know V10=13770 therefore Vo=32397.17399

the book says the initial cost is $32397.17

however i rounded up and said the initial cost is $32397.18

reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.

Who would be right in this case and whats the best thing to do in these situations ?

[knightrider]

This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.

What if in a question something is depreciating instead of compounding  , whats the rule then?

Would it just be  

[knightrider]

For this question attached i have a query.

i got the equation as Vn=(0.918)^n x Vo

now we know V10=13770 therefore Vo=32397.17399

the book says the initial cost is $32397.17

however i rounded up and said the initial cost is $32397.18

reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.

Who would be right in this case and whats the best thing to do in these situations ?

This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.

What if in a question something is depreciating instead of compounding  , whats the rule then?

Would it just be  

Can anyone help with these ? 

[plato]

Guys, how do I go about doing this one?

Definitely missing something simple here. The answer is A but I keep getting something completely different.

As a.t has said, there is an error here if we say there are 52 weeks in a year (which is what I expect VCAA would want you to assume; although 52 weeks is only 364 days.)
I used the calculator finance solver to find FV when interest is charged:
weekly = $26,112.69 as a.t. found
fortnightly = $26,225.78
monthly = $26,491.17
quarterly = $27,495.78
annually = $32,400.73
The closest answer on offer is A.

[plato]

For this question attached i have a query.
i got the equation as Vn=(0.918)^n x Vo
now we know V10=13770 therefore Vo=32397.17399
the book says the initial cost is $32397.17
however i rounded up and said the initial cost is $32397.18
reason is because when you sub my initial cost value into the equation you have a value of at least $13770.
where as  when you sub in the books initial cost value into the equation you have a value of less than $13770.
Who would be right in this case and whats the best thing to do in these situations ?

The book value after 10 years is likely to have been rounded to the nearest ten dollars. Therefore, it would make more sense for the question to ask for the initial cost of the machine rounded at least to the nearest dollar, if not the nearest ten dollars. You would expect greater clarity in a text book and I would think an exam question would avoid the issue. Given all this, I would round the answer here to the nearest cent.

[plato]

This rule for the effective interest  rate(attached) is for when n is  the number of times the interest compounds each year.
What if in a question something is depreciating instead of compounding  , whats the rule then?
Would it just be  

The study design only links the topic of effective interest rates to investments or loans. Therefore, I don't think application to depreciation is an issue to worry about.
The format of the formula for effective interet rate is slighly different to what VCAA has published on the new formula sheet in their sample exam papers for 2016. Find this on the VCAA website on the same page as you would look to find past further maths exam papers.

[knightrider]

The book value after 10 years is likely to have been rounded to the nearest ten dollars. Therefore, it would make more sense for the question to ask for the initial cost of the machine rounded at least to the nearest dollar, if not the nearest ten dollars. You would expect greater clarity in a text book and I would think an exam question would avoid the issue. Given all this, I would round the answer here to the nearest cent.

The study design only links the topic of effective interest rates to investments or loans. Therefore, I don't think application to depreciation is an issue to worry about.
The format of the formula for effective interet rate is slighly different to what VCAA has published on the new formula sheet in their sample exam papers for 2016. Find this on the VCAA website on the same page as you would look to find past further maths exam papers.

Thanks so much plato 

[knightrider]

If you were to use the financial solver on the CAS how would you show working out , on the paper?

Say the question was worth like 3marks.

[plato]

Just show the labelled list of values for N, I, PV etc