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sparrow2
 one year ago
need help
sparrow2
 one year ago
need help

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sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0question is about compound interest. \[a=p(1+r/m)mt and a=p(1+r)t\]

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0symbols are ordinary, why this two result arn't the same?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0a=p(1+r/m)^mt a=p(1+r)^t

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry, I don't know your answer since I'm not good with financial mathematics

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[a=p \left( 1+r \right)^t\] 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.

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0i know that ,but they must be equal, i think so

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, for first year principal is same during whole year. but in second case principal is different for every month.

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0so 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?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0@Palmo4ka esli mojesh pomogi :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let 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.

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0i understand that man, but why did you diveded anual rate by 12,is it ok?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@sparrow2 Do you speak Russian?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0kaneshna gavariu, no po angliski luchshe :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0а я, наоборот, говорю лучше порусски:) @sparrow2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0rate 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

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0so the answers will be different when calculating anualy and monthly?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0and dividing by periods is ok? so do they mean so when asking for periods(we know only annualy)

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0@Palmo4ka potomushto ti iz rossi( no ia net)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am sorry i don't understand your language fully,i am an indian.

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0i'm also not native speaker :D

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0so you divided it by 12 or by 6 and so on(anual rate) is it ok?

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0so 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but at the sametime multiply t by 12

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0i thought that this was just 2 different ways,but the answers must be the same, i thougt so

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no ,as you see principal goes on changing for compound interest.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0It might be enlightening to see what happens if you calculate the interest every day, every hour, every second..

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0@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 )

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0pe^rt will be if its continous

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Haha 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

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Notice that we get that continuous formula by letting \(m\to \infty\) in the discrete version : \[\large \lim\limits_{m\to\infty}~p\left(1+\frac{r}{m}\right)^{mt} = pe^{rt} \]

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0yeah i see, it easy to prove :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0Letting \(p=r=t=1\), we get the definition of euler constant \(e\) : \[\large \lim\limits_{m\to\infty}~\left(1+\frac{1}{m}\right)^{m} = e\]

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0yeah that is cool way to define e :) creative

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0okay thanks @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0that is indeed one of the most useful definitions of \(e\) https://en.wikipedia.org/wiki/E_(mathematical_constant)#History

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0so when you have like 12% anualy can you always say that monthly will be like 1 % @ganeshie8

sparrow2
 one year ago
Best ResponseYou've already chosen the best response.0oh i closed the question
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