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.Com
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.




RELATED QUESTIONS

An employee wants to invest ​$60 comma 00060,000 in a pension plan. One investment... (answered by Alan3354)
Milena deposited ​$6 comma 000 in a certificate of deposit​ (CD) account that (answered by ikleyn)
You have ​$440 in an account which pays 4.2 ​% compounded annually.... (answered by jorel1380)
An actor invested some money at 7​% simple​ interest, and ​$26 comma... (answered by ikleyn)
Mitch and Bill are both age 75. When Mitch was 22 years​ old, he began depositing... (answered by Boreal)
How long​ (in years and​ months) will it take for an investment to double... (answered by greenestamps)
Jerome will be buying a used car for ​$5 comma 5,000 in 4 years. How much money... (answered by Alan3354)
An investment company pays 6 %compounded semiannually. You want to have $ 23000 in the... (answered by addingup)
Suppose an investment account is opened with an initial deposit of $10500 earning 6.25%... (answered by greenestamps)