If you deposit $1,000 in an account that pays 6% annual interest compounded continuously, what will the balance be after five years?

Question

kuoministers · Answer

any idea how to formulate a equation for that?

anonymous · Answer

no :/ cantremember

mertsj · Answer

I believe the formula is 
$$A = Pe ^{rt}$$

kuoministers · Answer

Conpound interest can be calculated using the formula

kuoministers · Answer

attachment

kuoministers · Answer

P = principal amount (the initial amount you borrow or deposit)
r  = annual rate of interest (as a decimal)
t  = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n  =  number of times the interest is compounded per year

kuoministers · Answer

remember your interest compounds annually(every year)

mertsj · Answer

@Kuoministers That is indeed the formula for compound interest where you have a finite number of compounding periods.  However, in this problem, the interest is compounded continuously.  So the formula I posted is the one to use and I am afraid you are confusing the asker.  
Why don't you google "interest formula compounded continuously"?

anonymous · Answer

@Mertsj is right .

kuoministers · Answer

ah yes my bad @mertsj :)

kuoministers · Answer

but it still would work if you used the formula that i had?

mertsj · Answer

So Rugtugba, now that we have cleared the chatter, are you ready to continue?

anonymous · Answer

yes

mertsj · Answer

@Kuoministers What would you use for n?

kuoministers · Answer

1 since its compounded yearly

mertsj · Answer

Plug into the formula.  The initial amount A is 
Ok.  Let me deal with the cat first.

anonymous · Answer

lol

mertsj · Answer

@Kuoministers So compounded continuously means annually?  I thought compounded annually meant compounded annually.  Silly me!!

mertsj · Answer

Good luck, Rugtugba.  We have way too many cooks in this kitchen.

tkhunny · Answer

@Kuoministers the continuous forumla is the limiting form of the finite form you have posted.  Your calculus will have to be up to speed to prove it.  You can explore it on your own by calculating the finite formula multiple times, each with an increasing value of n.

anonymous · Answer

its alright guys i found it its 1349.60 thanks anyways