Question

Look way down for NEW QUESTION

Answer 1

Basically, you will have:
5000 (1+6/2)^(2n) where n is the number of years.

Answer 2

It should be 5000 [1+(6%/2)]^(2n)

Answer 3

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.......

Answer 4

Yea....6%/2.

Answer 5

Because 6% is "annual" and compounding happening half yearly.

Answer 6

Because it is compounded semi annually... you'll get interest every half a year

Answer 7

@Callisto 5000 [1+(6%/2)]^(2n) gives the amount ... but there is one fault I realized earlier

Answer 8

Yes, i think ?!, It is a GS with common ratio = 1.03

Answer 9

The earlier formula gives the sequence of a year .. not in six months I think
5000 [1+(6%/2)]^n ... will model sequence better

Answer 10

@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

Answer 11

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

Answer 12

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.

Answer 13

its

\[5000(1.03^{2n} + 1.03^{2n -1} + 1.03^{2n -2} + 1.03^{2n -3}...\]

n represents the 6 month compounding period.

Answer 14

he's doing it from the other end ... this is how this sequence ends.

Answer 15

6%/2=0.06/2=0.03, so they are the same.

Answer 16

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.

Answer 17

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.

Answer 18

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.

Answer 19

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

Answer 20

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.

Answer 21

Sorry your tab wasnt working.

Answer 22

so what's the question?

Answer 23

TO speak truth im confused myself. :l

Answer 24

As GT is saying, 5000(1+0.03)^n must be it.
im still not sure. sorry

Answer 25

Sorry but it's pretty confusing.

Answer 26

What is a sequence?

Answer 27

Is this a sequence: 1,6,11,16,21,26,...

Answer 28

What about this:
2^1, 2^2, 2^3, 2^4...

Answer 29

Isn't that exactly what the question requires?

Answer 30

The question says to write a sequence that represents the amount of money....

Answer 31

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.

Answer 32

Well, if GT says it's not a sequence, take it up with him because I think it is a sequence.

Answer 33

yes. It is a sequence.

Answer 34

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.

Answer 35

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.