## sparrow2 one year ago need help

1. sparrow2

question is about compound interest. $a=p(1+r/m)mt and a=p(1+r)t$

2. sparrow2

symbols are ordinary, why this two result arn't the same?

3. sparrow2

a=p(1+r/m)^mt a=p(1+r)^t

4. sparrow2

@Michele_Laino

5. anonymous

@.Gjallarhorn.

6. Michele_Laino

I'm sorry, I don't know your answer since I'm not good with financial mathematics

7. sparrow2

@Abhisar

8. sparrow2

@amistre64

9. sparrow2

@empty

10. anonymous

$a=p \left( 1+r \right)^t$ here interest is compounded annually $a=p \left( 1+\frac{ r }{ m } \right)^{mt}$ here interest is compounded monthly. or we can say interest of first month is also principal for next month and so on.

11. sparrow2

i know that ,but they must be equal, i think so

12. anonymous

no, for first year principal is same during whole year. but in second case principal is different for every month.

13. sparrow2

so if i have r as anual rate, and they tell me to fing future value of smt,but intereset must be monthly ,what i will do?

14. sparrow2

@Palmo4ka esli mojesh pomogi :)

15. anonymous

let us take the case principal=100 rate=12% annually then amount after first month $a=100\left( 1+\frac{ .12 }{ 12 } \right)^1=101$ amount after second month $a=101\left( 1+\frac{ .12 }{ 12 } \right)^1=101*1.01=102.01$ .......... this becomes principal for third month and so on. we see principal increases every month. but in the first case principal is same whole year.

16. sparrow2

i understand that man, but why did you diveded anual rate by 12,is it ok?

17. anonymous

@sparrow2 Do you speak Russian?

18. anonymous

no

19. sparrow2

kaneshna gavariu, no po angliski luchshe :)

20. anonymous

а я, наоборот, говорю лучше по-русски:) @sparrow2

21. anonymous

rate is annual ,but we are calculating every month so we divide by 12 if we have to calculate after every 6 months,we divide by 2 if we have to calculate every 3 months ,we divide by 4

22. sparrow2

so the answers will be different when calculating anualy and monthly?

23. anonymous

yes

24. sparrow2

and dividing by periods is ok? so do they mean so when asking for periods(we know only annualy)

25. sparrow2

@Palmo4ka potomushto ti iz rossi( no ia net)

26. anonymous

i am sorry i don't understand your language fully,i am an indian.

27. sparrow2

i'm also not native speaker :D

28. sparrow2

so you divided it by 12 or by 6 and so on(anual rate) is it ok?

29. sparrow2

so if i have anual rate like 12%, if they askme me to calcualte anualy i use 12%,but by monthly i will use 1% and the answers will be different

30. anonymous

correct

31. anonymous

but at the sametime multiply t by 12

32. sparrow2

i thought that this was just 2 different ways,but the answers must be the same, i thougt so

33. anonymous

no ,as you see principal goes on changing for compound interest.

34. sparrow2

on earth :)

35. sparrow2

okay thanks man :)

36. anonymous

yw

37. ganeshie8

It might be enlightening to see what happens if you calculate the interest every day, every hour, every second..

38. sparrow2

@ganeshie it's true. you see, if you increase periods the amount is increasing too(it's more beneficila for banks to use more periods :D )

39. sparrow2

pe^rt will be if its continous

40. ganeshie8

Haha these days most banks calculate interest continuously(every nano second or so) The interest wont increase much by increasing the periods, it saturates after 12 periods or so

41. ganeshie8

Notice that we get that continuous formula by letting $$m\to \infty$$ in the discrete version : $\large \lim\limits_{m\to\infty}~p\left(1+\frac{r}{m}\right)^{mt} = pe^{rt}$

42. sparrow2

yeah i see, it easy to prove :)

43. ganeshie8

Letting $$p=r=t=1$$, we get the definition of euler constant $$e$$ : $\large \lim\limits_{m\to\infty}~\left(1+\frac{1}{m}\right)^{m} = e$

44. sparrow2

yeah that is cool way to define e :) creative

45. sparrow2

okay thanks @ganeshie8

46. ganeshie8

that is indeed one of the most useful definitions of $$e$$ https://en.wikipedia.org/wiki/E_(mathematical_constant)#History

47. sparrow2

so when you have like 12% anualy can you always say that monthly will be like 1 % @ganeshie8

48. sparrow2

oh i closed the question