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Mathematics 44 Online
OpenStudy (anonymous):

What is the formula for compound interest, WITHOUT adding the principal?

OpenStudy (anonymous):

for continuously compounding it is\[e^{rt}\]

OpenStudy (anonymous):

where r is the rate of growth, and t is the time

OpenStudy (anonymous):

so here's a question: Somebody borrows $249 from a bank. the bank charges compound interest at 1.7% per month. Calculate how much interest she has at the end of three months.

OpenStudy (anonymous):

so r is your rate which is 1.7% and t is your time which is 3 months \[249\times(e ^{.017\times3})\]

OpenStudy (anonymous):

262.0284004

OpenStudy (anonymous):

that is the total so the interest is just 262.0284004-249 = $13.0284

OpenStudy (anonymous):

to express it as a percent you just use the first equation way up top all alone. Make sense? So you made over 5% in three months. e^(.017x3)=.052322891

OpenStudy (anonymous):

sorry the bank made over 5%

OpenStudy (anonymous):

thanks a lot! :)

OpenStudy (anonymous):

just remember that formula. You'll use it a lot, I promise you.

OpenStudy (anonymous):

wait - what is e?

OpenStudy (anonymous):

what kind of calculator do you have?

OpenStudy (anonymous):

in front o you

OpenStudy (cruffo):

couple notes: general compound interest formula (daily, monthly, semiannually, annualy, ... anything other that "compounded continuously") \[A=P\left(1+\frac{r}{n}\right)^{nt}\] A = amount after investment P=principle r = interest rate (as a decimal) n = number of times compounded per year t = time (in years)

OpenStudy (cruffo):

"monthly" => n = 12 "three months =>t = 3/12 = 0.25 \[A = 249\left(1+\frac{0.017}{12}\right)^{(0.017)\cdot (0.25)}\] Then the interest in three months will be A-249

OpenStudy (anonymous):

in the problem she said 1.7% a month, not annually.

OpenStudy (cruffo):

ahh, wording...I read to mean "compounded monthly"

OpenStudy (cruffo):

The formula Quantabee using is to "compound continuously" \[A = Pe^{rt}\] and t is always in years.

OpenStudy (anonymous):

as long as your r is scale to the proper interval of t it should not matter right? So if my rate was in months, and my t was in months...then I am fine with this formula.

OpenStudy (cruffo):

such as \[A = 249(1+0.017)^3\] Then the interest would be A-P.

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