superannuation (1 Viewer)

[Kutay]

hey i am doing 3 unit maths and i am doing all the 2unit past papers but yeh i have forgotten the superannuation formula and my texts book are at a mates place can anyone help me out please thankyou

 

[Kutay]

heh

dont worry got it

 

[Xayma]

There is no superannuation formula. What happens is you modify the compound interest formula (A=P(1+r/100)ⁿ) and create a series of it.

For example: Tom invests $10 at the start of every year into his superannuation fund find how much he will have at the end of the 10th year. Assuming that his superannuation has a rate of 5% pa and is compounded annually.

Let A_n be the amount at the end of the n^th year
A<Sub>1</sub>=10(1.05)¹
A₂=(10+A₁)(1.05)¹
=10(1.05¹+1.05²)
etc.

 

[Kutay]

Question

i Think the answer is wrong here have a look:

"On 1 Jan 1999, a person joins a supa fund by investing $2000 at 12% p.a. compound interest. She invests $2000 at the beginning of each year until she retires on 31 dec 2019. Show that the accumulated value of the investment on retirement is $183 005 correct to the nearest dollar"

Thats the question i keep getting $163 397 to nearest dollar?
is the answer wrong or is there a trick in the wording here or something please help thankyou

 

[Kutay]

so can anyone tell me how to do it ?

 

[Trev]

i'll hav a look n do it for u.....i forget how this stuff works

 

[Trev]

just wondering, did you have the length of time as 20 years? (coz dates can trick ppl, ie. 2019-1999 = 20) because it is actually 21 years....

 

[Trev]

i cant b bothered writing out the A1, A2 etc, but this is what you shoudl have:
A = 2000[(1.12)^21 + (1.12)^20 + .... + (1.12)^1]
the geometric series gives:
S21 = [1.12(1.12^21 - 1)]/(1.12 - 1)

therefore total amount:
A = 2000 * S21
= 2000*{[1.12(1.12^21 - 1)]/(1.12 - 1)}
= $183005.1676
to the nearest dollar = $183,005

 

[Kutay]

oh ok thankz yeh i got 21 but when i did the gp thiny like i put the 1.12^21 in the brackets not outside thankz

 

[Trev]

dats k! put as many q's up as u want

 

[goan_crazy]

is this part of series and sequenceS?
this looks hard =/
we onli jus started series yesterday
were up to aritmetic progressions

 

[Trev]

it aint hard, and its applications of series and sequences, "superannuation"

 

[goan_crazy]

alrite...well sure if i hav problems i know where 2 come trev

 

[Kutay]

Another question heh

A person jumps on a trampoline from a height of 3m. he then bounces up to 2 1/4 metres and on each subsequent bounce he rises to 3/4 of his previous height. what is the total distance he covers?

 

[Trev]

= 3 + 2( 9/4 + 9/4(3/4) + 9/4(3/4)^2 +......)
= 3 + 2(a/(1-r))
= 3 + 2([9/4]/[1-3/4])
= 3 + 2(9)
= 21 metres total distance covered

 

[Kutay]

Thankyou very much hmm i am going to go to bed now it is getting fairly late :|

 

[Trev]

u do that..............*cough*