Question 1121519: How much more will an investment of $15 comma 000 earning 5.5 % compounded continuously for 7 years earn, compared to the same investment at 5.5 % compounded monthly for 7 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! an investment of 15,000 compounded continuously for 7 years uses the formula:
f = p * e^(rn)
p = principal or present value
f = future value
r = interest rate per time period
n = number of time periods.
in your problem, this equation becomes f = 15,000 * e^(.055*7)
solve for f to get:
f = 22,044.21482
an investment of 15,000 compounded monthly for 7 years uses the formula:
f = p * (1+r)^n
f = future value
p = principal or present value
r = interest rate per time period
n = number of time periods.
time period is in months.
take annual interest rate and divide it by 12 to get .055/12 per month.
take number of years and multiply them by 12 to get 7*12 = 84 months.
in your problem, this equation becomes f = 15,000 * (1 + .055/12) ^ (7*12)
solve for f to get:
f = 22,024.83315
compare that to continuous compounding which gets you f = 22,044.21482.
continuous compounding gives you 22,044.21482 minus 22,024.83315 equals 19.38167648 more dollars in interest than monthly compounding.
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