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

7 years agofor continuously compounding it is\[e^{rt}\]

7 years agowhere r is the rate of growth, and t is the time

7 years agoso 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.

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

7 years ago262.0284004

7 years agothat is the total so the interest is just 262.0284004-249 = $13.0284

7 years agoto 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

7 years agosorry the bank made over 5%

7 years agothanks a lot! :)

7 years agojust remember that formula. You'll use it a lot, I promise you.

7 years agowait - what is e?

7 years agowhat kind of calculator do you have?

7 years agoin front o you

7 years agocouple 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)

7 years ago"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

7 years agoin the problem she said 1.7% a month, not annually.

7 years agoahh, wording...I read to mean "compounded monthly"

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

7 years agoas 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.

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

7 years ago