I know I learned this in eighth grade but I forgot it. What is the formula for figuring out compound interest? I know e is in there somewhere.
Thanks.
I think this is what you are looking for:
FV=PV(1 + i)^n
where:
PV = present value
FV = future value
i = interest rate in percent per period
N = number of periods
Hope this helps.
Depends on if you are just figuring interest on one original sum of money, or whether you are making continuint regular contributions. For the former it goes like this:
[(number of periods per year + interest rate)/number of periods per year] to the power equal to number of periods interest is being figured to. Awkward wording, I’ll try an example. periods per year is 4, interest reate is 5%, figured for three years, so powered to 12(=34)
(4.05/4)to the 12th power Answer is 1.16 This figure is then multiplied by the original sum, say $250.00, so 2501.16=$290
If you are making continuing regular contributions it is [(1+i)powered to number of contributions -1/i]c. with i being equal to interest rate and c being the amount of the contributions. So if you put $50 per month into an account that earns 4% interest annually, and do this for 18 months, you come up with [(1.00333)to 18th power-1/.00333]50. or $925.96
Wish I knew how to makes the formulae clearer on this computer.
Sounds like you’re talking about interest compounded continuously, which is
FV = Pe[sup]rt[/sup].
FV = future value
P = principal
r = interest rate
t = time
I can’t help on the OT, but maybe I can shed a little light on formula formatting. If you use the “sup” VB markup you can superscript, which will make exponents much more readable. For example, “E=mc[ sup ]2[ /sup ]” (with the spaces removed from the brackets) produces E=mc[sup]2[/sup].
There are no stupid math questions; only stupid math.
Does anyone know which method banks use? Do they actually break the interest into daily amounts, then raise that to the power of the number of days? Or do they use the exponential formula?
There are also two other similar compound interest formulas if you deposit something each month then its:
a = p * Sum{(1+i/x)^n,n = 0, t - 1}
a = accumulated amount
p = payment per month
i = interest rate PA
x = how many compounding periods in a year
t = how many times its compounded
If you are paying off a loan then its:
a = d(1+i/x)t - p*Sum{(1+i/x)n,n = 0, t - 1}
a = amount remaining
d = amount owing
Banks pretty much only use software to calculate interest, IIRC (my mother is a banker), if something is compounded such as monthly, and someone wants to make a withdrawl or get a bank statement they calculate it up to that day (ie. the 6th if february is 7/28 or 1/4 months), otherwise interest isn’t added until the end of the month.
What an odd occurrence … the response to two sequential but unrelated threads can be almost the same.
This works for both :
and
Stupid Math Question
(although the math question’s already been answered, I thought I’d post this anyway)
Whatever has happened with usage of the word ‘differential’ outside of the technical fields[sup]*[/sup], the distinction between difference and differential is still quite meaningful in at least one mathematical sense. Difference equations are for discrete steps (differences), differential equations are for the continuous case (as you probably know, the differential works using infinitesimal differences).
As an example, consider compound interest : If you compound it at regular intervals – say r% a year, you wait until a year is up, then multiply by the rate and add to it to get the new amount.
This gives you the difference equation
V[sub]n+1[/sub] = V[sub]n[/sub] * ( 1 + r/100)
The solution to this difference equation for any V[sub]n[/sub] is :
V[sub]n[/sub] = V[sub]0[/sub] * (1 + r/100)[sup]n[/sup]
where V[sub]0[/sub] is the starting principal. This is the same formula that diamud posted.
But if instead of computing the interest after the period of time, you computed it continuously, you’d get the differential equation
v’ = r*v with v(0) = P, the starting principal,
and v’ denotes the time derivative of v. The solution to this equation is :
v = P**e*[sup]rt[/sup] (which was posted by Cabbage)
It all depends on how you compute the interest, although as you make the interval smaller in the discrete, you of course come closer to the continuous case. Most credit card companies that I know of compound daily (check the fine print).
For more information, there’s a free (GNU copyleft) textbook titled “Difference Equations to Differential Equations” available in postscript and PDF formats at http://math.furman.edu/~dcs/book/
panama jack
[sup]*[/sup] Anyone who uses “American sports” as a singular conscious entity is pushing the language just a little bit, BobT. I don’t find these changes in language objectionable.
in the immortal words of my 10th grade algebra teacher :
“There are no stupid questions, only stupid people who ask questions.”
or
“Your mind is too small too be wandering off by itself.”
Actually, in Ireland, for home loan payments, some banks calculate interest daily, while others calculate it monthly. For my car loan, it’s on a quarterly basis.
There’s a big difference between, say, 6% compounded daily and the “same” rate monthly, which is worth keeping an eye on.
That’s the one I wanted. Thanks a bunch.