SOLUTION: 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%?

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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