Re: Sort of off topic, but please help?
Re: Sort of off topic, but please help?
- Subject: Re: Sort of off topic, but please help?
- From: Charles Srstka <email@hidden>
- Date: Thu, 24 Jan 2002 01:46:44 -0600
Whoops! You are correct. I left out the carat. D'oh! Stupid typo...
On Thursday, January 24, 2002, at 12:39 AM, email@hidden wrote:
I think this is the formula for continuous interest:
P*(e^(t*r))
Nick
Well, let's see. I start with an initial principal. Let's call it P. I
have an interest rate, r, and a time t. With simple interest, the
amount I end up with is P + Prt or P(1+rt). However, you're dealing
with compound interest, so it's going to be more complicated than
that. Let's see how far we can get without knowing the formulas
(formulae?)...
I'll do interest compounded annually first, because it's simpler.
Again, we start out with P. After one year, I've got P(1+rt), and if t
is in years, we can plug in 1 year for t in that equation, and our
amount of cash at the end of year 1 will be P(1+r), which will be used
as P for the interest for the next year. Therefore, plug it in to the
simple interest equation and you get (P(1+r))(1+r) or P(1+r)^2 at the
end of year 2. Plug that into the simple interest equation again, and
you get P(1+r)^3 at the end of year 3. I'm seeing a pattern here -
from this I think that we can safely deduce that the formula for
interest compounded *annually* would be P(1+r)^t, as long as the value
of t is in years. This equation looks familiar to me, although I have
gathered quite a bit of interest since the last time I looked at that
equation, so you may want to double-check it. :-)
Now, if it is compounded monthly, hmm... let's see.
Well, our rate r will still be an annual rate, so it would probably be
best to keep t in years. 12 months in a year, so each period would be
1/12 of a year. Okay:
At the end of one month, we've got P(1+rt) = P(1+r(1/12)) = P(1+r/12)
at the end of month 1. Plug this in for another month, and we get:
P(1+r/12)
(1+rt) = P(1+r/12)(1+r(1/12)) = P(1+r/12)^2. Hmm, the same pattern
emerges, although now our rate is divided by 12, and the exponent is
the number of months instead of years. The number of months is, of
course, 12t, if t is in years, so I think we can generalize this
formula as P(1+r/
12)^(12t), right?
Looking at this again, we can generalize this to any number of times
the interest is compounded per year, by assigning that number to n and
making the formula read P(1+r/n)^(nt). I believe this is the formula
for compound interest, but again you may want to double-check it
against something.
The last type of interest is continuous interest. Let's see. I suppose
that I would find the limit of the compound interest function as n
approaches infinity. For some reason, I'm having a brain fart and I
can't figure out how to solve this one symbolically at the moment.
However, if you just plug in values and keep plugging in bigger and
bigger values for n, you will notice the thing tend toward P*e(rt), so
I would guess that that would be the formula for continuous interest.
With the interest formulas, you should hopefully be able to find
whatever you want to find using algebra.
Hope that at least some of this helps...
Charles
On Wednesday, January 23, 2002, at 07:30 PM, email@hidden wrote:
I think I'm doing this so that it's compounded monthly... It's been
so long since I've done this in math, and unfortunately, I don't have
any math textbooks except my Calculus one... I should be writing
programs that use Calculus... I'm much more familiar with it :-)
Thanks for your help!
On Tuesday, January 22, 2002, at 11:37 PM, Charles Srstka wrote:
It would depend on whether you're calculating simple interest,
compound interest (in which case we'd need to know whether it's
compounded annually, monthly, etc.), or continuous interest.
You should be able to find the formulas for calculating interest in
any junior-high math textbook.
On Wednesday, January 23, 2002, at 12:36 AM, email@hidden wrote:
Hello all,
I'm trying to write my first official non-tutorial Cocoa
program (a loan calculator for my dad) and this question is
directed towards the business / math type of people.
Does anyone know of any way to calculate the interest rate of a
loan, paid monthly, when you know the initial principle, the
monthly payments made (interest + principle paid), and the number
of years that the loan lasts (12 payment periods per year)?
It's not really essential, but I would like to know this and I
didn't know where else to ask...
Thanks!
-Kevin
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