VCE General & Further Maths Question Thread!

[dream chaser]

Hi Guys,

Need help with this question

Question: Roslyn earns an annual salary of $54200,which is paid monthly. She did not join the superannuation fund until her 37th birthday and she now pays 7% of her gross salary to the superannuation fund. Her employer contributes a further 14%.

(a) What amount of money is placed each month into her superannuation fund?
This question I am able to do. I did:
21/100 x $54200 = $11382. Then $11382/12 = $948.50 per month.

Now this is where I got stuck...

(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.

(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

So basically I need help with part (b) and (c) with this question. Also, if anyone reads this, could you please read a couple of my previous posts on the Further Maths Questions Thread to see whether I am able to complete a previous question of mine. It was in regards to PV and FV and the topic was on annuity investments(I posted it yesterday).

All the help will be much appreciated. Thanks. By the way, Merry Christmas to Everyone for yesterday. 

[Aaron]

Thank you very much dream chaser for helping us to assist you, by providing working out and your explanations. It is much appreciated that you've taken the time to read my post and acknowledge it.

[dream chaser]

Thank you very much dream chaser for helping us to assist you, by providing working out and your explanations. It is much appreciated that you've taken the time to read my post and acknowledge it.

No problem Aaron  .

[PhoenixxFire]

I don't think that PV will be zero as the investment will not simply increase by not giving anything to the bank/insurace company in the first place. The answer is $81939.67.

The PV will be zero because they're asking how much he will have in total after 10 years of saving. Unless otherwise stated, this means you can assume that he starts with 0 savings. Putting 0 as the PV will give you an answer of $81939.67

Hi Guys,

Need help with this question

Question: Roslyn earns an annual salary of $54200,which is paid monthly. She did not join the superannuation fund until her 37th birthday and she now pays 7% of her gross salary to the superannuation fund. Her employer contributes a further 14%.

(a) What amount of money is placed each month into her superannuation fund?
This question I am able to do. I did:
21/100 x $54200 = $11382. Then $11382/12 = $948.50 per month.

Now this is where I got stuck...

(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.

I would just put this into the finance solver on your CAS
N=276
I(%)=4.2
PV=0
Pmt=-948.50
FV=?
PpY=12
CpY=12
PmtAt=END

Which gives the answer that FV=439829.26

It probably is possible to work out without CAS, but you shouldn't need to.

(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

So basically I need help with part (b) and (c) with this question. Also, if anyone reads this, could you please read a couple of my previous posts on the Further Maths Questions Thread to see whether I am able to complete a previous question of mine. It was in regards to PV and FV and the topic was on annuity investments(I posted it yesterday).

All the help will be much appreciated. Thanks. By the way, Merry Christmas to Everyone for yesterday. 

Your solution for this is fine, you just used the wrong value. Replace $2487.90 with $439829.26 and it'll give you the correct answer.

[Lear]

Hey Dream Chaser!
Echoing Aaron's comments above, thank you for showing your approach. Trust me when I say you will learn much better by recognising where you went wrong instead of simply being told what to do.

(b) The superannuation fund pays 4.2% per annum compound interest, compounded monthly. Assuming that Roslyn's annual salary remains constant, what is the amount of superannuation she will have available at her 60th birthday?

This is the way I did it, bare in mind this method is completely wrong as I got the wrong answer in the end.

Vn=R^n x V0, where R=1+r/100
Vn=R^n x 948.50
R=1+r/100
r=4.2/1=0.35% monthly rate
R=1+0.35/100  1.0035

Vn =(1.0035)^n x 948.50

V276=(1.0035)^276 x 948.50
V276 = $2487.90

Therefore my answer is $2487.90. However the actual answer to this question is $439829.26. Can someone please show me how to get this answer.

So for a superannuation, essentially the person starts of with a sum of money, and each month the employer adds an amount of money to the fund which compounds over time. Where you went wrong is that you treated the 948.50 as the initial value when it is not. The initial value is actually simply 0 while 948.50 is the amount of money added each month.
Because of the monthly addition you cannot raise the R value to a power n as each the month the V value is changing.
Here's the recurrence formula for this superannuation.
Vn+1=R*Vn + 948.50.
Now due to the additional 948.50 added every month, doing this formula 250+ times will take a while...
Luckily, you have your CAS!
Here's the inputs I used
N: 276 (12 months multiplied by (60-37) years)
I: 4.5 (This is always in percentage per annum and it is 4.5 from the question)
PV: 0 (There's no information on the initial value of the fund so we assume 0)
PMT: -948.50 (948.50 is being invested into the fund by the employer hence we use the negative)
FV: ?
CPY/CPY: 12

The future value is found to be $439829.26

(c) Suppose that when Roslyn retires at 60 years of age, she places her superannuation in a perpetuity that will provide a monthly income without using any of the principal. If the perpetuity pays 4.25% per annum compounding monthly, what monthly payment will Roslyn receive?

My answer is completely wrong as I used the answer I obtained in part (b) for this.
D=r/100 x V0
r=4.25%/12
r=0.354167% monthly rate.
D=0.354167/100 x $2487.90
D=$8.81.

Therefore my answer is $8.81. The answer obtained in the book is $1557.73. How do I get that answer?

Your working out is almost perfect. You just forgot to divide the 4.25 by 100 as you stated in the first line. The r should instead be 0.003542
Now we just need to multiply by the value from C which is 439829.26
This gives us 1557.73 as required.

You could also do this on financial solver
N: 1 (we just want to see the value of one payment)
I: 4.25%
PV: -439829.256 (from c and it is negative because it's an investment)
PMT: ? (we don't know)
FV: 439829.256 (Perpetuity value stays the same and hence FV is just positive value of PV)
PPY/CPY: 12

PMT = 1557.73

***Beaten by PF but i'll leave this as some of the financial solver explanations may be useful for understanding.

[dream chaser]

Thank you both PhoenixxFire and Lear for the help. My apologies for not thanking you both earlier. Just a quick question. I don't understand why PV wouldn't equal -948.50. Isn't 948.50 how much the person initially invests which gets bigger over time. Also, this is an Annuity Investment right?

[Lear]

948.5 is not how much the initial investment is. It’s how much is being added by the employer every month.


Your super annual Annuation is there to support you once you retire.  Think of it as a retirement piggy bank. You start earning it when you start working. Your employer contributes to the piggy bank every month and it slowly piles up over time. Initially, of course, there was nothing in this piggy bank. However it starts adding up every time your employer adds another 948.50 to it. Once you retire you’re going to break open that piggy bank and it’ll support you

[dream chaser]

948.5 is not how much the initial investment is. It’s how much is being added by the employer every month.


Your super annual Annuation is there to support you once you retire.  Think of it as a retirement piggy bank. You start earning it when you start working. Your employer contributes to the piggy bank every month and it slowly piles up over time. Initially, of course, there was nothing in this piggy bank. However it starts adding up every time your employer adds another 948.50 to it. Once you retire you’re going to break open that piggy bank and it’ll support you

Okay. How come in my question it says that Roslyn pays 7% of her gross salary to the superannuation. Does this mean she alongside her employer is adding money into her superannuation fund or still only the employer each month. Also, does your last post informing me how a superannuation work apply for all superannuation's?

Is this how it works? So at the start, Roslyn starts with $0.00. Then after one month, she has $948.50. As 4.2%p.a /12 =0.35% monthly rate and 0.35/100 x $948.50 = $3.32. Then this gets added on to the $948.50 which makes $951.83. Therefore, she will have $951.83 in her superannuation account after one month. And this process continues every month right?

MOD EDIT: merged two consecutive posts. Try not to double post

[MB_]

Okay. How come in my question it says that Roslyn pays 7% of her gross salary to the superannuation. Does this mean she alongside her employer is adding money into her superannuation fund or still only the employer each month.

Yes, in this example both Roslyn and the employer contribute to Roslyn's super.

Is this how it works? So at the start, Roslyn starts with $0.00. Then after one month, she has $948.50. As 4.2%p.a /12 =0.35% monthly rate and 0.35/100 x $948.50 = $3.32. Then this gets added on to the $948.50 which makes $951.83. Therefore, she will have $951.83 in her superannuation account after one month. And this process continues every month right?

Almost, after one month she will have $948.50. After two months she will have 948.50*2=$1897 plus the interest on the first month amount (=$3.32) which is equal to $1900.32. This process continues each month.

[dream chaser]

Yes, in this example both Roslyn and the employer contribute to Roslyn's super.Almost, after one month she will have $948.50. After two months she will have 948.50*2=$1897 plus the interest on the first month amount (=$3.32) which is equal to $1900.32. This process continues each month.

Why wouldn't the first month be $951.82?

If V0 didn't equal zero, then there would be interest in the first month right?

[MB_]

Why wouldn't the first month be $951.82?

If V0 didn't equal zero, then there would be interest in the first month right?

I think you answered your own question. The first month isn't $951.82 as there wasn't any money in the super to gain interest over that time (as V0=0). You're correct in saying if V0 didn't equal zero, then there would be interest in the first month.

[marangutan]

Hey can anyone please tell me if I've done these two questions correctly?

https://imgur.com/a/vmHFYo8
(took me way too long to try and attach this picture lol)

Sorry, for the second question, I change my answer to 84 months

[MB_]

Hey can anyone please tell me if I've done these two questions correctly?

https://imgur.com/a/vmHFYo8
(took me way too long to try and attach this picture lol)

Sorry, for the second question, I change my answer to 84 months

The first part looks right but why did you change your answer to 84 months in the second part?

[marangutan]

The first part looks right but why did you change your answer to 84 months in the second part?

Thank you
Yeah my bad lol. What I did originally was round the year down first, then convert to months

[marangutan]

Need help with question c please!
https://imgur.com/a/VJvY0V2
I'm not sure whether the answer is 1407 or 1408 players. Here is my thinking: if you plug in the numbers into the equation, you get 1407.37488.

As soon as 1 year elapsed, there will be 1407.37488 players. So if you round it down to 1407 players, this means that 1 year has not passed yet. However if you round it up to 1408 players, 1 year has already elapsed.
My working out is a bit messy to comprehend, but hopefully you understand