Compound Interest

Date: 05/30/2001 at 00:11:59
From: Brandon Winters
Subject: Compound Interest

I need a formula (or maybe more than one) to compute compound 
interest, with the known variables of:  

  pmt = payment amount
    b = current (or begining) balance
   ni = frequency of compounding the interest 
 npmt = frequency of payments made
    i = interest rate.

The results that I am looking for are: d = duration until balance is 
paid in full, and amti = the total amount of interest paid.

I have: 
                       (1 + r/n)NT - 1 
B = A (1 + r/n)NT - P*------------------
                        (1 + r/n) - 1  

where 
B = balance after t years
A = amount borrowed
n = number of payments per year
P = amount paid per payment
r = annual percentage rate

however, with this the interest is compounded at the same frequency 
that the payments are made (n). 

Please help - I am stuck.

Date: 05/30/2001 at 04:05:48
From: Doctor Mitteldorf
Subject: Re: Compound Interest

Brandon -

You can adapt the formula you already have, based on the compounding 
frequency you want to use.  

If the compounding frequency is LESS FREQUENT than the payment 
frequency, the effect is moot because the payment is already made, the 
balance is reduced, and there is nothing to compound.

If the compounding frequency is MORE FREQUENT than the payment 
frequency, and compounding frequency is a constant multiple of payment 
frequency, you can handle this by adjusting the interest rate.

For example, if payments are quarterly and compounding is monthly:
Let r be the nominal annual rate.
Then r/12 is the amount charged each month.
(1+r/12) is the multiplicative factor for each month.
(1+r/12)^3 is the multiplicative factor for each quarter.
(1+r/12)^3-1 is amount charged each quarter.
4*{(1+r/12)^3-1) is the effective annual rate.

Use this latter quantity in place of your annual rate in the formula 
you already have to correct for the fact that interest is compounded 
monthly though payments are quarterly.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/