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sparrow2

  • one year ago

need help

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  1. sparrow2
    • one year ago
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    question is about compound interest. \[a=p(1+r/m)mt and a=p(1+r)t\]

  2. sparrow2
    • one year ago
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    symbols are ordinary, why this two result arn't the same?

  3. sparrow2
    • one year ago
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    a=p(1+r/m)^mt a=p(1+r)^t

  4. sparrow2
    • one year ago
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    @Michele_Laino

  5. 0_0youscareme
    • one year ago
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    @.Gjallarhorn.

  6. Michele_Laino
    • one year ago
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    I'm sorry, I don't know your answer since I'm not good with financial mathematics

  7. sparrow2
    • one year ago
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    @Abhisar

  8. sparrow2
    • one year ago
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    @amistre64

  9. sparrow2
    • one year ago
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    @empty

  10. anonymous
    • one year ago
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    \[a=p \left( 1+r \right)^t\] 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
    • one year ago
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    i know that ,but they must be equal, i think so

  12. anonymous
    • one year ago
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    no, for first year principal is same during whole year. but in second case principal is different for every month.

  13. sparrow2
    • one year ago
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    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
    • one year ago
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    @Palmo4ka esli mojesh pomogi :)

  15. anonymous
    • one year ago
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    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
    • one year ago
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    i understand that man, but why did you diveded anual rate by 12,is it ok?

  17. anonymous
    • one year ago
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    @sparrow2 Do you speak Russian?

  18. anonymous
    • one year ago
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    no

  19. sparrow2
    • one year ago
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    kaneshna gavariu, no po angliski luchshe :)

  20. anonymous
    • one year ago
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    а я, наоборот, говорю лучше по-русски:) @sparrow2

  21. anonymous
    • one year ago
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    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
    • one year ago
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    so the answers will be different when calculating anualy and monthly?

  23. anonymous
    • one year ago
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    yes

  24. sparrow2
    • one year ago
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    and dividing by periods is ok? so do they mean so when asking for periods(we know only annualy)

  25. sparrow2
    • one year ago
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    @Palmo4ka potomushto ti iz rossi( no ia net)

  26. anonymous
    • one year ago
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    i am sorry i don't understand your language fully,i am an indian.

  27. sparrow2
    • one year ago
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    i'm also not native speaker :D

  28. sparrow2
    • one year ago
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    so you divided it by 12 or by 6 and so on(anual rate) is it ok?

  29. sparrow2
    • one year ago
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    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
    • one year ago
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    correct

  31. anonymous
    • one year ago
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    but at the sametime multiply t by 12

  32. sparrow2
    • one year ago
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    i thought that this was just 2 different ways,but the answers must be the same, i thougt so

  33. anonymous
    • one year ago
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    no ,as you see principal goes on changing for compound interest.

  34. sparrow2
    • one year ago
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    on earth :)

  35. sparrow2
    • one year ago
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    okay thanks man :)

  36. anonymous
    • one year ago
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    yw

  37. ganeshie8
    • one year ago
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    It might be enlightening to see what happens if you calculate the interest every day, every hour, every second..

  38. sparrow2
    • one year ago
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    @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
    • one year ago
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    pe^rt will be if its continous

  40. ganeshie8
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yeah i see, it easy to prove :)

  43. ganeshie8
    • one year ago
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    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
    • one year ago
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    yeah that is cool way to define e :) creative

  45. sparrow2
    • one year ago
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    okay thanks @ganeshie8

  46. ganeshie8
    • one year ago
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    that is indeed one of the most useful definitions of \(e\) https://en.wikipedia.org/wiki/E_(mathematical_constant)#History

  47. sparrow2
    • one year ago
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    so when you have like 12% anualy can you always say that monthly will be like 1 % @ganeshie8

  48. sparrow2
    • one year ago
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    oh i closed the question

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