Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

262.0284004

Answer 6

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

Answer 7

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

Answer 8

sorry the bank made over 5%

Answer 9

thanks a lot! :)

Answer 10

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

Answer 11

wait - what is e?

Answer 12

what kind of calculator do you have?

Answer 13

in front o you

Answer 14

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)

Answer 15

"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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

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