Monthly Saving

Date: 08/13/97 at 15:33:29
From: dneath
Subject: Establishing payment

Can you please supply the formula to allow the calculation of the
regular monthly saving required to accumulate a known Required Balance
at a point in the future? Simply: Fund value/Term in months but
allowing for compound interest being added to the regular savings on 
an annualised basis, this evaluation to start with the Known Fund 
Value Required.

Date: 08/13/97 at 16:50:34
From: Doctor Anthony
Subject: Re: Establishing payment

Suppose we want the value to be $50,000 in 25 years and the compound 
interest rate to be 9 percent per year.  We shall take this to give a 
monthly interest rate of (9/12 = .75) percent (very small error).  

Let $P be the monthly payments; then the calculation of P is as 
follows:

  P[1 + 1.0075 + 1.0075^2 + ..... + 1.0075^299] = 50000

   P[1.0075^300 - 1]
   -----------------  =  50000
     1.0075 - 1

                          50000 x .0075
                    P =  ---------------
                         1.0075^300 - 1

                   
                      =  $44.60 

Clearly you can adapt the calculation for different total sums and 
interest rates, but the method should be clear from the calculation 
given above.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/