Re: Compound Interest


"Axel Vogt" <test3@xxxxxxxxxxx> wrote in message
news:4479E9E3.25C6725B@xxxxxxxxxxxxxx
Theriel wrote:

Hello.
I've got a task to create a formula to compare two fixed-term deposit
accounts.

So:
p - principal
r1/2 - rate of interest in the first/second bank
n1/2 - number of times the interest is compounded in the first/second
bank

Usually, when a bank gives an interest rate, it is the interest paid in one
year. And also, when a compounding period is given, it gives the number of
periods in a year (e.g., daily--365 times a year, weekly-52 times a year or
monthly--12 times a year). So the intrerest paid per compounding period is
i1/2 = (r1/2)/(n1/2) where ri is the interest rate in decimal percent ( e./g
5% = 0.05)

So, comparing:
p(1+r1)^n1 (1+r1)^n1
----------- = ---------
p(1+r2)^n2 (1+r2)^n2

This should be

p(1+i1)^n1 (1+i1)^n1 (1+r1/n1)^n1
--------------- = ------------ = --------------
p(1+i2)^n2 (1+i2)^n2 (1+r2/n2)^n1

And the limit as the number of periods becomes very large

limit (n-->oo) (1+(r/n))^n -->e^r = exp (r)

So the ratio becomes approximately e^(r1-r2)

The problem is - how can I simplify the last formula? I was informed
that it _is_ possible to do it but I just can't find it out... I tried
with rewriting (1+r1)^n1 using binomial coefficient but it didn't change
anything.

I would be grateful for any hint, suggestion, solution...

Thank you for help,
Theriel

A common way is to convert to exp(rates*time) for each period
or otherwise stated: determine the present value or discount
factor.

Usually there are more conventions to be obeyed (day counting,
holidays, to be payed in advance etc). The discount factor will
respect all these (like for a zero bond, not defaultable).


.

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