We know that to determine the EAR which is basically the annual interest rate for compounding frequencies with the adjustments you have to compute the following
$$EAR =\left ( 1+\frac{\text{ annual interest rate } }{\text{ compounding periods }} \right ) ^{\text{compounding periods}}-1$$
Now when take the limit of shorter and shorter compounding periods meaning continuous compounding we get a formula $ EAR = e^r-1$
Where r is the annual interest rate

Question

We know that to determine the EAR which is basically the annual interest rate for compounding frequencies with the adjustments you have to compute the following
$$EAR =\left ( 1+\frac{\text{ annual interest rate } }{\text{ compounding periods }} \right ) ^{\text{compounding periods}}-1$$ 
Now when take the limit of shorter and shorter compounding periods meaning continuous compounding we get a formula $ EAR = e^r-1$
Where r is the annual interest rate

mimi_x3 · Answer

@dan815 How did they derive that formula for continuous compounding from the original equation?

dan815 · Answer

cuz

mimi_x3 · Answer

Not sure if i was clear ...-.- so like ask me questions if i didnt make sense

dan815 · Answer

write a differential eqn

dan815 · Answer

wait ill brb.. u try to clarify the question as much as u can

dan815 · Answer

ok bacck

mimi_x3 · Answer

Basically as the compounding periods increase ... lets say from quaterly to annually to monthly and then to daily ... the EAR becomes greater and greater ... and it kinda converges at compounding period of 365
Basically the second formula finds the value it converges to

dan815 · Answer

ya okay

dan815 · Answer

basically umm the normal compounding formula is
Total=P*(1+r)^n

dan815 · Answer

then we when u got annual rate being compounded nominally over a period of tie

mimi_x3 · Answer

Ya im trying to find the total interest rate after adjustments meaning with compunding periods

dan815 · Answer

Total=P*(1+r/k)^(n*k)

mimi_x3 · Answer

yes

dan815 · Answer

now u wanna see what happens as k goes to infinite

mimi_x3 · Answer

when k goes infinite

mimi_x3 · Answer

and not exactly with this formula

mimi_x3 · Answer

but with the formula discussing the interest accrued over the year with compounding periods

dan815 · Answer

hmm im thinkg about like

mimi_x3 · Answer

k when it says the interest is 8% compounding quaterly ... that basically more than 8% interest over the yr

dan815 · Answer

binomial series expansiosn

dan815 · Answer

but i dont remember getting growth rates like that

dan815 · Answer

like another way to think about it... okay look you had a continous growth rate

dan815 · Answer

and u got some rate after 1 year

dan815 · Answer

we can write a DE for that

mimi_x3 · Answer

BTWWWW

mimi_x3 · Answer

PLS READ MY FORMULA

dan815 · Answer

ya i se theres -1

mimi_x3 · Answer

No n meaning number of years isnt included

dan815 · Answer

oh okay u wanan see for 1 year rightq

mimi_x3 · Answer

its just abt the interest and compounding periods

mimi_x3 · Answer

yes

dan815 · Answer

ok!

mimi_x3 · Answer

hahaha :P

dan815 · Answer

lemme ask  uthis

dan815 · Answer

after 1 year, like after the total compounding period in 1 yeasr

dan815 · Answer

would you expect 
A=p(1+r)

dan815 · Answer

like lets say its 12% being compounded continously

mimi_x3 · Answer

Nope

dan815 · Answer

okay i see

dan815 · Answer

what wud u expect in 1 year?

mimi_x3 · Answer

hmmmm lemme take a pic of my work one sec

mimi_x3 · Answer

http://puu.sh/fFP73/a353d27252.jpg

dan815 · Answer

okay i see

mimi_x3 · Answer

So basically i showed u that the more its compounded then the more the interest is per year

mimi_x3 · Answer

but then it converges at daily obv

mimi_x3 · Answer

And its showing that u cld use the formula e^r-1 to find the convergence

dan815 · Answer

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