Question

need help

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

@Michele_Laino

Answer 5

@.Gjallarhorn.

Answer 6

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

Answer 7

@Abhisar

Answer 8

@amistre64

Answer 9

@empty

Answer 10

\[a=p \left( 1+r \right)^t\]
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.

Answer 11

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

Answer 12

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

Answer 13

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?

Answer 14

@Palmo4ka esli mojesh pomogi :)

Answer 15

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.

Answer 16

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

Answer 17

@sparrow2 Do you speak Russian?

Answer 18

no

Answer 19

kaneshna gavariu, no po angliski luchshe :)

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

yes

Answer 24

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

Answer 25

@Palmo4ka potomushto ti iz rossi( no ia net)

Answer 26

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

Answer 27

i'm also not native speaker :D

Answer 28

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

Answer 29

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

Answer 30

correct

Answer 31

but at the sametime multiply t by 12

Answer 32

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

Answer 33

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

Answer 34

on earth :)

Answer 35

okay thanks man :)

Answer 36

yw

Answer 37

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

Answer 38

@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 )

Answer 39

pe^rt will be if its continous

Answer 40

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

Answer 41

Notice that we get that continuous formula by letting \(m\to \infty\) in the discrete version :

\[\large \lim\limits_{m\to\infty}~p\left(1+\frac{r}{m}\right)^{mt} = pe^{rt} \]

Answer 42

yeah i see, it easy to prove :)

Answer 43

Letting \(p=r=t=1\), we get the definition of euler constant \(e\) :

\[\large \lim\limits_{m\to\infty}~\left(1+\frac{1}{m}\right)^{m} = e\]

Answer 44

yeah that is cool way to define e :) creative

Answer 45

okay thanks @ganeshie8

Answer 46

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

Answer 47

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

Answer 48

oh i closed the question