series help (1 Viewer)

[Farmerism]

two men A and B commence work on an annual salary of $10000. A recieves an increment of $1000p.a whilst B receives an increment of $500 each 6 months

who has recieved the greater amount after ten years, and by how much?






... how can there be any difference? if each man recieves an increment of 1000pa anyway... (500 *2 since 6months is half a year)

if someone understands it coudl they please provide working

thanks

 

[Riviet]

Is that all the information you are given in the question?

 

[vanush]

trick question@!

 

[Farmerism]

yeah thats all the info that I have, however the question was photocopied from some coroneos book set A.S.1 (i do 2u maths, but my teachers a lostie so it could either be from the 3u or 2u book) so if someone has that book can they clarify whether or not its the whole question (i think it is anyway)


i foudn that if you use the simple arithmetic formula and use months instead of years for B's income, then that produces a differnt result to A's which is calculated in years. however this still didnt give me the answer (though i was close! by a 1000 difference or something)

anyway that was just an idea that perhaps we just havent thought of the right method to use. yet.

 

[SoulSearcher]

Maybe if we go along by this method.
Person A receives $10000 in year 1, $11000 in year 2, $12000 in year 3 and so on until receiving $19000 in year 10. Therefore the total amount of money he has received is, using the sum of a arithmetic series,
S_n = n/2 * (a+l), where a is first term and l is last term
S₁₀ = 10/2 * (10000+19000)
= 5 * 29000
= $145000
Person B receives $10000 per year, regardless of pay rates. He also receives $500 every 6 months, making 20 payments of $500 each in those 10 years. So total amount he receives in those 10 years are:
$10000 * 10 + $500 * 20
= 100000 + 10000
= $110000
Therefore person A receive more money, to the tune of $145000 - $110000 = $35000 dollars.
Not sure if this works though, I haven't done these types of questions for a while now.

EDIT: Fucked it up here. Please ignore

 

[Farmerism]

hm the answer thats written on the sheet is that B will recieve the greater amount by $2500

 

[SoulSearcher]

Back to the drawing board.

 

[drynxz]

Try considering this:

Man A:
1st year: 10000
2nd year: 11000
3rd year: 12000 and so on therefore series is:
10000,11000,12000 etc. with difference 1000

Man b: (try splitting into 6 month payments)
1st year: {5000 + 5500} = 10500
2nd year: {6000+6500} = 12500
3rd year: {7000+7500} =14500
so your series is:
10500,12500,14500 etc. with difference 2000

try that?