Question 1027731
compounded annually, the formula is:


f = p * (1+r)^n


f is the future value
p is the present value
r i the interest rate per time period (per year).
n is the number of time periods (years).


at 5%, with a p of 10,000, for 20 years, the formula becomes:


f = 10,000 * (1.05)^20 = 26532.98


compounded continuously, the formula is:


f = p * e^(rt)


f =  future value
p = present value
r = interest rate per time period (per year).
n = number of time periods (years).


with p = 10,000 and r = .05 and t = 20, the formula becomes:


f = 10,000 * e^(.05*20) = 27182.82


continuous compounding is the most compounding you can do.


the more compounding periods per year, the closer you get to continuous compounding.


for example, if you compounded daily, then:


assume 365 days per year.


p = 10,000
r = .05/365 = .000136986301 per day.
n = 20 * 365 = 7300 days.


formula becomes:


f = 10,000 * (1.000136986301)^7300 = 27180.95669


that's a lot closer.


if you compounded per hour, you would get much closer.


the limit is continuous compounding.


you can't get a higher value than continuous compounding.