Simple example: A bank offers me just 1% annual underlying interest on a certain account. If there is no compounding, and if I put in $100 at the start of the year, then a year later I can withdraw $101. How much can I withdraw if it is continuously compounded? $102.71?
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If interest in compounded n times a year, the accumulation factor for 1 year is
a(n) = (1 + i/n)^n
lim n-->∞ a(n) = e^i
So your answer is 100e^i = 101.00501
So at that low rate of interest, it hardly makes any difference. It would round up to 1 penny.
Steve A
I = P*e^(rt)
I = interest
P = principal
e = the constant 2.71828 (to five decimal places)
r = interest rate as a decimal (5% is expressed as .05)
t = time
r and t must use the same units. If r is the interest rate per year, t must be expressed in years.
I and P also must use the same units. If P is in US dollars, so is I.
The principal and interest must be added to find the end amount.
P(t) = P(0)*(1 + e^(rt)) where P(t) is the amount at time t, and P(0) is the beginning amount.