Look way down for NEW QUESTION

- anonymous

Look way down for NEW QUESTION

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

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

- Callisto

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

- 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.......

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

Yea....6%/2.

- anonymous

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

- Callisto

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

- experimentX

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

- Callisto

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

- 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

@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

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

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

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

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

- anonymous

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

- 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

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

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

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

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

Sorry your tab wasnt working.

- saifoo.khan

so what's the question?

- saifoo.khan

TO speak truth im confused myself. :l

- saifoo.khan

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

- saifoo.khan

Sorry but it's pretty confusing.

- Mertsj

What is a sequence?

- Mertsj

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

- Mertsj

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

- Mertsj

Isn't that exactly what the question requires?

- Mertsj

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

- 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

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

- Mertsj

yes. It is a sequence.

- 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

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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.