I need some help!

OK, rosala...look at this.....

Notice that if I have 3³, I'm just really doing this.......3 * 3  * 3 = 27

So, look at our "formula"

We have ........4096 x (1 + r/n)^nt .......note that the interest rate given is 12.5%.......but that's the rate for a yearly compounding.....we must divide this by 2, because we are compounding on a half-year basis !!!!

So...n = 2  (the number of compoundings per year) and r/n =12.5/2 = .0625........with me, so far????

Now...look at the "nt" exponent........n is the number of copoundings per year and t is the number of years. So, if we compounded for 1 + 1/2 years, that would be 3 compoundings   (2 the first year and one more for the next half-year !!). So, "nt" just  equals    (2 times / year)*(1 +1/2 years) = 3 times !!!

OK.......let's put all of this together...we have......

4096*(1 + .0625)³ ......notice that the expression in the parentheses is really just   1.0625........so this gives us........4096*(1 .0625)³

Now, forget the "4095" part and let's just look at the (1 .0625)³  part.....note what this really says is similar to our 3³ example earlier....it says that we really have this:

(1.0625) * (1.0625) * (1,0625).......so now, let's add the "4096" part back and we have.....

4096 *(1.0625) * (1.0625) * (1,0625)    ...so......the first compounding is represented by the first multiplication......and 4096 * 1.0625 = 4352...and that's how much we have after one compounding (i.e., after the first half-year)

And the next multiplication  is just  taking this amount and multiplying again by 1.0635 = 4352 * 1.0625 = 4624...and this is the amount after the second compounding (i.e., one year).

So the final multiplication is just our accumulted anount (4624) multiplied again by 1.0625 = 4913 !!!! And that's the amount after 1 +1/2 years  !!!!!

Note that the result is growiing ever larger......hence the term, "compounding"

Also.....note that it would be extremely tedious using my example method if we had to calculate half-year compoundings for 30 years......we would have to multiply the initial amount by 1.0625 .......60 tmes !!!!

Fortunately....the modern calculator relieves us of this burden with the use of the x^y key !!!

Does all this "resolve" the "mystery" some ????

4096 if he gave it for 12 1/2% per annum interest being componded half yearly?

OK , rosala....since the interest is being compounded twice a year we need to adust it to 12.5%/2 = 6.25% =  .0625 

So we have

A = 4096(1 +.0625)^(nt)       where n is the number of years  and t is the number of times compounded per year.....in this case, 2

So this simplifies to

A = 4096(1 +.0625)^(n*2) 

You didn't specify the number of years in your question....if you can give me that, I'll do an edit and compute the amount for you !!!

but CPhill , the question was given like this only and nothing more!my teacher did it using 6 months as i remember , maybe that n represents something else too or maybe u can decrease the rate to half according to half year and give no years!do u have any particular way of own to solve this?

OK, rosala....we can do it for 6 months.....then n will just equal (1/2)  (half  a year) in the equation

So we have

A = 4096(1 +.0625)^((1/2)*2) =

A = 4096(1 +.0625)^(1) =  Rs 4352  

This make sense....we just compounded the amount 1 time (for just 1/2 of a year) !!!

Does that help??

CPhill but when i checked at the back of the book , the final answer isnt this , it is coming 4,913 .

i really cant understand it!i shall read your answer when i return!now im off to school!so bye!

OK, rosala...now that I know what the "book answer"  is .......the compounding was for 1.5 years!!

Here's the proof

A = 4096(1 + .0625)^(1.5*2) =

A = 4096(1 + .0625)^(3) = Rs 4913

So....there you go.......

CPhill!i cant understand your answer!is there any other way?

rosala:  (I don't want to barge in but CPhill doesn't seem to be on line right now.)

I beleive that your instructor just gave you a partial formula, perhaps to ease you into this type of problem.  The complete formula is:                   A = P(1 + r/n)^(n·t)

where n represents the number of times that the money is compounded per year and t is the number of years.

Also, to get the answer that your book has requires compounding for 1 1/2 years.

If you solve this:  A  =  4096(1 + .125/2)^(2·1.5)  you will get 4913.

If you weren't given the 1 1/2 year part, then you can't get the answer.

Wow , that was amazing CPhill!thanks for your answers CPhill  and geno , i must give u both some points!