SOLUTION: 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

Algebra ->  Inverses -> SOLUTION: 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       Log On


   



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) About Me  (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.