[jay_shark]

Pretty much what Omaha said but I'll expand some more .

When we talk about compound interest , we have a familiar formula A = P(1+r/n)^(nt)

P = Principal amount
r= annual interest rate
n = the number of compounded periods per annum .
t= t years


The above formula may be re-written as

A= P*[(1+r/n)^(n/r)]^(rt)
Substitute n/r = x

A= P*[1+1/x)^x]^(rt)

So as x becomes large , the quantity (1+1/x)^x approaches e.

A=p*e^(rt)

Example : Find the amount after 3 years if $1000 is invested at an interested rate of 12% per annum compounded continuously .

Solution : Using A=P*e^(rt) , r=0.12 and t=3,
A=1000*e^(0.12*3)
A= $1433.33