Question 1027731: How much more would $10,000 earn in 20 years in an account compounded continuously than an account compounded annually if the interest rate on both accounts is 5%?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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