VCE General & Further Maths Question Thread!

[Zealous]

Business Maths Question - help appreciated.

James and Jamie have just finished repaying a 5 year, $8000 reducing balance loan.
During the first year interest was debited monthly at 8.5% p.a.; during the next 2 years the rate fell to 8% p.a. but rose to 8.3% p.a. for the remaining period of the loan.
Before signing their contract James and Jamie were also given the option of fixing the interest rate at 8.25% p.a. (debited monthly) for the term of the loan.
By considering the total amount of interest that they paid, determine whether James and Jamie made the right decision in choosing the variable interest rate for the loan rather than the fixed rate.

Answers

Fixed: Interest = $1790.20
Variable: Interest = $1784.51 so correct decision is the variable, by $5.69

First of all, this is a ridiculously long question. It's highly unlikely you'll get a question this difficult in the exam unless I've taken a really long approach (haven't done business maths in ages....) The finance solver entries work off each other, so take your time looking through what I've changed in each calculation.

Let's first calculate the amount of interest using the fixed rate of interest, then calculate the interest using the variable interest rate.

Fixed Interest Rate (using Finance Solver for Ti-nspire): We need to find the monthly payment, so input all the given information.
n=60 (5 years multiplied by 12 months per year)
I=8.25
Pv=8000
Fv=0
Ppy=12
Pmt=-163.17

To find out how much interest we are paying, multiply the payment by the amount of payments and subtract the value of the loan:
Interest (fixed rate)= 163.17x60-8000=1790.20

So using the fixed interest rate, we pay $1790.20 interest.

Variable Interest Rate: We again need to find the monthly payment, but we need to split this loan up into three different sections. 1: Interest of 8.5% for 1 year. 2: Interest of 8% for 2 years. 3: Interest of 8.3% for 2 years.
1a: first find the payment if the interest stayed at 8.5% for five years.
n=60
I=8.5
Pv=8000
Fv=0
Ppy=12
Pmt=-164.1323

1b: find the future value if that payment lasted only one year.
n=12
I=8.5
Pv=8000
Ppy=12
Pmt=-164.1323
Fv=6658.9675

2a: find the payment for the next four years with interest rate 8% if the payments went for all the years.
n=48
I=8
Pv=6658.9675
Fv=0
Ppy=12
Pmt=-162.5649

2b: find the future value if the $162.56 payment only lasted 2 years.
n=24
I=8.5
Pv=6658.9675
Ppy=12
Pmt=-162.56
Fv=3594.3973

3: find the final payment to complete the loan (2 years) at 8.3%.
n=24
I=8.3
Pv=3594.3973
Fv=0
Ppy=12
Pmt=-163.0571

So how much interest does he pay for the 5 year loan with the variable interest rate?
164.1323 x 12 + 162.5649 x 24 + 163.0571 x 24 - 8000 = 1784.52

Fixed Interest: 1790.20
Variable Interest: 1784.52
So they save $5.68 by choosing the Variable Interest loan and hence it was the right decision.

Note: I got a slightly different answer (1 cent) because of the large amount of calculations, so I think they rounded in between steps.

Hope that helps!

[Jono_CP]

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[PsychoT]

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Using Finance Solver:

N= 5x12 = 60 (interest debited monthly, solving for value after 5 years)
I= 12% (just the interest rate)
PV= 65000 (the amount of the loan, positive value as you are receiving the money, would be negative if you are making an investment, etc, giving it away for a fixed period of time)
Pmt= -715.71 (regular payments, negative as you are paying them)
FV= ____ (the amount of the principle left to be repaid after the 5 years)
PpY= 12 (amount of compounding periods per year, as it's monthly, value is 12 in both PpY and CpY)
CpY= 12

Don't have my calculator, but if you solve for the future value, that's what will still be owing after 5 years.

[NeedHelpWithStudy]

Help with Attached question please. Don't know how to do it.

[Splash-Tackle-Flail]

I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense

[PsychoT]

I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense

I think they round each sac to out of 20 or 40, at least that's what they do at my school.

[LiquidPaperz]

Im pretty sure that they take the mark out of 20,40 etc and record it, then get a mark out of 100 after adding everything and send the proportion out of 100 to VCAA

[keltingmeith]

I'm not sure if I'm allowed to post here for questions that aren't math ones in a sense, but just wondering, when our sac marks are rounded, do they take the total of all our sac marks, proportionate it to a mark out of 100, then round, or do they round the mark of each sac to out of 20 or out of 40 for each sac separately? hope it makes sense

It depends what each SAC is worth. Refer to the study design for assistance.

For unit 3, you do 2 SACs - an application task and an analysis task. The application task is worth (15+20+5)/60, and the analysis task is worth (15+5)/60. Your actual percentage is multiplied by this weightings, added together, and multiplied by the overall unit 3 SAC weighting of 20%.

For unit 4, you do two analysis SACs, and both are worth (7+8+5)/40. So, your actual percentage is multiplied by these weightings again, added together, and multiplied by by the overall unit 4 SAC weighting of 20%.

Then, those two final marks are added together, and that's your SAC contribution.



Why is finding the SAC contribution this tedious? Because VCAA has nothing better to do than crunch random numbers for thousands of students. I'm not quite sure how the schools submit your marks, it might be a SAC-by-SAC submission to make it easier on VCAA.

[Stressedyear11here]

Hi,
Can a line of regression tell us if there is a relationship between two variables?

The scatter plot shows no relationship, and the regression line gradient is about 2, and r = 2.0

Thanks

[kinslayer]

Hi,
Can a line of regression tell us if there is a relationship between two variables?

The scatter plot shows no relationship, and the regression line gradient is about 2, and r = 2.0

Thanks

The regression line is used to estimate the linear relationship between two variables.

The gradient of the regression line is not relevant in determining the strength of the relationship- what is relevant is how well the line fits the data, which is usually measured by r^2. r is always between -1 and 1, so I'm not sure how you got r = 2.0.

The scatter plot usually gives you a reasonably good idea of how strong the (linear) relationship is. Once you have found the correct value for r (and r^2), you will probably find that it is close to zero.

[Splash-Tackle-Flail]

Thanks everyone! I think I get it, I asked my teacher and apparently we just round it off for each sac, where the application task mark becomes a mark out of 20, and the data one is out of 40

[LiquidPaperz]

The cost($C)of renting a car is given by C =an+b where:
n is the number of kilometers travelled
a is the cost per kilometres travelled and
b is a fixed cost

For a person travelling 200 km, the cost of car rental is $430. For a person travelling 315 km, the cost of car rental is $660. The values of a and b are:

[keltingmeith]

This is an example of simultaneous equations. For person 1, and for person 2, . By substitution, . Substituting that into the equation for person 1, .

[engton1796]

Question relating to trigonometry and geometry.

The following diagram shows a cross-sectional view of a beehive with its regular hexagonal compartments. 
Only shows one triangle within a hexagonal compartment and the base at 10mm
Determine the value of an interior angle of each hexagonal compartment,  as shown in the diagram.

I put down 360/6 = 60 degrees,  but this was marked wrong.  How do you calculate this the right way?

[Jono_CP]

Can someone help with this problem please? Ones in black pen thanks!