questions - help appreciated (3 Viewers)

[lyounamu]

Q A fund is established to provide basketball team's annual Awards night.
$10000 is placed in the fund one year before the first Award night. It is decided that $450 will be withdrawn each year. The money is invested at 3% per annum and compounded annually.

It also decided to increase the amount of money withdrawn from each year by 2% per annum.

This is quite a different question to what I have been doing. I tried to come up with a relationship or connection of some sort but it's quite hard. Can anyone help me on this?

 

[shaon0]

Q A fund is established to provide basketball team's annual Awards night.
$10000 is placed in the fund one year before the first Award night. It is decided that $450 will be withdrawn each year. The money is invested at 3% per annum and compounded annually.

It also decided to increase the amount of money withdrawn from each year by 2% per annum.

This is quite a different question to what I have been doing. I tried to come up with a relationship or connection of some sort but it's quite hard. Can anyone help me on this?

I_1=10000[(1+0.03)]^n-450*d(n-1)) where n=1, d=0.02
I_2=10000[(1+0.03)]^n-450*d(n-1)) where d=0.02 where n=2
etc.
What are we trying to find out?

 

[lyounamu]

I_1=10000(1+0.03)-450
I_2=10000(1+0.03-d)-450 where d=0.02
What are we trying to find out?

Sorry, you are trying to find the amount of money left after 25th award night

But your line of working is not right though.

Mine is like

1st: 10000 x 1.03 - 450
2nd: 10000 x 1.03^2 - 450 x 1.03 - 450 x 1.02
3rd: 10000 x 1.03^3 - 450 x 1.03^2 - 450 x 1.02 x 1.03 - 450 x 1.02^2
4th: 10000 x 1.03^4 - 450 x 1.03^3 - 450 x 1.02 x 1.03^2 - 450 x 1.02 ^2 x 1.03 - 450 x 1.02^3
5th: 10000 x 1.03^5 - 450 x 1.03^4 - 450 x 1.02 x 1.03^3 - 450 x 1.02^2 x 1.03^2 - 450 x 1.02^3 x 1.03 - 450 x 1.02^4
nth: 10000 x 1.03^n - 450 x 1.03^(n-1) - .........(don't know)...............- 450 x 1.02^(n-1)

Then I realised some connections for some of the tems (e.g. the end terms) but I just couldn't find any connection for the middle terms.

 

[shaon0]

Sorry, you are trying to find the amount of money left after 25th award night

But your line of working is not right though.

Thanks, I'm getting no where with this. umm, do you know what the answer is?

 

[tommykins]

回复: Re: questions - help appreciated

man i find consumer arithmetic harder than 4u, seriously - it drives me fucking nuts.

 

[lyounamu]

Thanks,
I_25=10000[(1+0.03-d*(25-1))^25]-450 where d=0.02 where n=25
I_25=10000[(1+(0.03-(0.02^24))]^25-450
Thus, I_25=$9850 Am i right or wrong?

Nah that's not right. If you think about it, we originally had 10000 dollars with some interest (3% every year) and if we took out $450 (and that is increasing by 2% ) every year for 25 years, we should logically only have few hundred bucks if not few tens.

 

[shaon0]

Nah that's not right. If you think about it, we originally had 10000 dollars with some interest (3% every year) and if we took out $450 (and that is increasing by 2% ) every year for 25 years, we should logically only have few hundred bucks if not few tens.

Oh crap i read it as decreasing...crap sorry and then i read it again incorrectly.
my bad sorry.

 

[munch0r]

do you have an actual answer for this, so i can verify if i am right?

 

[lyounamu]

do you have an actual answer for this, so i can verify if i am right?

Yep. Feel free to post. I have an actual answer.

 

[shaon0]

Re: 回复: Re: questions - help appreciated

man i find consumer arithmetic harder than 4u, seriously - it drives me fucking nuts.

Yeah i don't get consumer arithmetic either.

 

[Iruka]

I think the middle terms form a GP with a= 450 x 1.03^(n-1) and the common ratio, r = 1.02/1.03.

 

[Timothy.Siu]

the above post is correct

let P = $10000 R= 1.03 Q=450 S=1.02

1st withdrawal- PR²-Q
2nd withdrawal- PR³-QR-QS
3rd withdrawal - PR⁴-QR²-QRS-QS²

nth withdrawal - PR⁽ⁿ⁺¹⁾ -QR^(n-1) -QR^(n-2) S-QR^(n-3) S²-......-QR(n-n)S^(n-1)

= PR⁽ⁿ⁺¹⁾ - Q(R^(n-1) -R^(n-2) S-.....-RS^(n-2) -S^(n-1) )
using the formula sum Nth = PR⁽ⁿ⁺¹⁾ - QR^(n-1) [(S/R)^{n -1})]/((S/R)-1)
therefore sum of 25th withdrawal = $456.41
around there

 

[lyounamu]

the above post is correct

let P = $10000 R= 1.03 Q=450 S=1.02

1st withdrawal- PR^2-Q
2nd withdrawal- PR^3-QR-QS
3rd withdrawal - PR^4-QR^2-QRS-QS^2

nth withdrawal - PR^(n+1)-QR^(n-1)-QR^(n-2)S-QR^(n-3)S^2-......-QR(n-n)S^(n-1)

= PR^(n+1) - Q(R^(n-1)-R^(n-2)S-.....-RS^(n-2)-S^(n-1))
sum Nth = PR^(n+1) - QR^(n-1)[(S/R)^n -1)]/((S/R)-1)
therefore sum of 25th withdrawal = $456.41
around there.

Yep, that's right. Thanks. Thanks to Iruka too for pointing that crucial information out!

 

[lyounamu]

P and Q are the points on the curve y=x^2. The x coordinates of P and Q are 2-h and 2+h respectively. Find
i) the equation of the secand PQ
(I did this part and I got y = 4x - 4 + h^2)
ii)The limiting position of this line as h -> 0
(I did this part as well and I got y=4x-4)
iii)Describe the geometrical significance of the limiting position in your own words.

I did this part as well but I am not sure if I explained it right, hear me out anyway:

The limiting position made it possible to find the equation of the tangent of y=x^2 as we approach x=2.

If you can explain better than I did, please post below because I am not sure if I can get a mark for this or not...what a stupid question...

 

[Iruka]

Sounds perfect to me. The whole idea of the tangent is that it is the limit of a series of secants.

 

[lyounamu]

Sounds perfect to me. The whole idea of the tangent is that it is the limit of a series of secants.

Thank you so much! I am relieved now.

 

[lyounamu]

Really weird question:

y = sinx/x

Use the trapezoidal rule to find the approximate area from 0 to 3 using 4 function values.

Ok, here is a problem:

They gave us a table but under 0, I don't know if I should write 1 or undefined. In the solution, they wrote it as 0 but can they just do that?

 

[shaon0]

Really weird question:

y = sinx/x

Use the trapezoidal rule to find the approximate area from 0 to 3 using 4 function values.

Ok, here is a problem:

They gave us a table but under 0, I don't know if I should write 1 or undefined. In the solution, they wrote it as 0 but can they just do that?

No, its undefined for x=0.

 

[lyounamu]

No, its undefined for x=0.

Yeah, it should be undefined or 1 (as x-> 0, sinx/x = 1)

 

[lyounamu]

Look at this confusing wording:

How do you interpret this:

Q. A total of 300 tickets are sold in a raffle which has three prizes. There are 100 red, 100 green and 100 blue tickets.

What is the probability that at least one of the winning tickets is not red.