anonymous
  • anonymous
Look way down for NEW QUESTION
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Basically, you will have: 5000 (1+6/2)^(2n) where n is the number of years.
Callisto
  • Callisto
It should be 5000 [1+(6%/2)]^(2n)
anonymous
  • anonymous
After first 6 months, you have: 5000 + 5000*3% After second 6 months you have: 5000 + 2*5000*3% + 5000*3%*3% After third 6 months you have: 5000 + 3*5000*3% + 2*5000*3%*3% + 5000*3%*3%*3% so on.......

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anonymous
  • anonymous
Yea....6%/2.
anonymous
  • anonymous
Because 6% is "annual" and compounding happening half yearly.
Callisto
  • Callisto
Because it is compounded semi annually... you'll get interest every half a year
experimentX
  • experimentX
@Callisto 5000 [1+(6%/2)]^(2n) gives the amount ... but there is one fault I realized earlier
Callisto
  • Callisto
Yes, i think ?!, It is a GS with common ratio = 1.03
experimentX
  • experimentX
The earlier formula gives the sequence of a year .. not in six months I think 5000 [1+(6%/2)]^n ... will model sequence better
Callisto
  • Callisto
@experimentX it depends how you define n, if n is the number of year, the above is correct. if n is the number of period, then your saying is correct
Callisto
  • Callisto
for 5000(1+.03)^1, 5000(1+.03)^2, 5000(1+.03)^3, 5000(1+.03)^4... you take every half year as 1 period, then it's @experimentX 's saying, and it's correct
experimentX
  • experimentX
yeah ... i have been giving the same kind of answer for sequence before ... lol. but sure it's sequence that has been asked so ... i guess this should be correct answer.
campbell_st
  • campbell_st
its \[5000(1.03^{2n} + 1.03^{2n -1} + 1.03^{2n -2} + 1.03^{2n -3}...\] n represents the 6 month compounding period.
experimentX
  • experimentX
he's doing it from the other end ... this is how this sequence ends.
anonymous
  • anonymous
6%/2=0.06/2=0.03, so they are the same.
anonymous
  • anonymous
What I gave is the "exact" accrued interest calculations at the end of each 6 month period. Campbell_st gave you the "simplified" and generalized geometric series you eventually get when you take my approach to "nth" period and do bunch of algebraic modifications.
anonymous
  • anonymous
That is not a sequence. That is simply the "formula" applied to different periods. 5000(1+0.03)^n gives you the TOTAL value of the initial investment from the time of investment to the end of the nth 6-month period. That is NOT a sequence.
anonymous
  • anonymous
Let us take the first year. You have two six month periods. After first 6 months, you have: 5000 + 5000*3% = 5000(1+0.03) After second 6 months you have further interest accrued on the interest amount from first period: 5000 + 2*5000*3% + 5000*3%*3% = 5000(1+2*0.03+(0.03)^2)) = 5000(1+0.03)^2 As you generalize that.....you end up getting 5000(1+0.03)^n for the nth period.
anonymous
  • anonymous
For example, at the end of third period, you get: 5000 + 3*5000*3% + 2*5000*3%*3% + 2*5000*3% + 5000*3%*3%*3% This is nothing but 5000(1+0.03)^3
anonymous
  • anonymous
Tn is the nth term. Since we established each first term gives you 5000 (1+0.03)^1, second term gives you 5000(1+0.03)^2 and third term gives you 5000 (1+0.03)^3 and so on.....you can generalize that the nth term gives you 5000(1+0.03)^n. As for the proof that is the case, it is a long complex expression that you can probably find by Google searching.
saifoo.khan
  • saifoo.khan
Sorry your tab wasnt working.
saifoo.khan
  • saifoo.khan
so what's the question?
saifoo.khan
  • saifoo.khan
TO speak truth im confused myself. :l
saifoo.khan
  • saifoo.khan
As GT is saying, 5000(1+0.03)^n must be it. im still not sure. sorry
saifoo.khan
  • saifoo.khan
Sorry but it's pretty confusing.
Mertsj
  • Mertsj
What is a sequence?
Mertsj
  • Mertsj
Is this a sequence: 1,6,11,16,21,26,...
Mertsj
  • Mertsj
What about this: 2^1, 2^2, 2^3, 2^4...
Mertsj
  • Mertsj
Isn't that exactly what the question requires?
Mertsj
  • Mertsj
The question says to write a sequence that represents the amount of money....
Mertsj
  • Mertsj
We already know that the formula will give the amount of money but the problem says to write a sequence that does the same thing.
Mertsj
  • Mertsj
Well, if GT says it's not a sequence, take it up with him because I think it is a sequence.
Mertsj
  • Mertsj
yes. It is a sequence.
Mertsj
  • Mertsj
Well sometimes you have to use your own common sense. You surely know what a sequence looks like. So when GT says it's not a sequence, use your own common sense.
anonymous
  • anonymous
There is clearly a confusion on what is being asked and said. What I am trying to explain is "how" you get 5000(1+0.03)^n and the compounding works by figuring out the terms for each compounding period. You don't get that by adding the terms of the sequence 5000(1+.03)^1, 5000(1+.03)^2, 5000(1+.03)^3, 5000(1+.03)^4..... It is by using first principles of compounding like I have shown in numerous posts above. I have no idea what use it is whether or not the following is a sequence: 5000(1+.03)^1, 5000(1+.03)^2, 5000(1+.03)^3, 5000(1+.03)^4... They are all obtained by properly compounding the interest on a principal amount. People who focus on "terminology" to the detriment of actually teaching first principles don't tap into the full potential - I believe.

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