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MathGroup Archive 1996

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Re: Financial Problems

  • To: mathgroup at
  • Subject: [mg5064] Re: [mg5059] Financial Problems
  • From: "Paul R. Wellin" <wellin>
  • Date: Fri, 25 Oct 1996 22:48:06 -0400
  • Sender: owner-wri-mathgroup at

> I have the student version of mathematica and the book"Mathematica by
> Example" which shows compoud interest etc. But I don't think any of the
> packages has functions for future of present value. Does anyone know
> anything about this?

The formula to compute the future value of an investment say,
consisting of n equal payments of D dollars, paying an interest
rate r per payment interval, is given by:

In[1]:= FutureValue[D_, n_, r_]:= D((1 + r)^n - 1)/r

So for example, the value of an annuity after 20 years
(or 20*12 = 240 months), in which you invest $100 per
month (the investment interval) in an account that pays
10% per year (or 10%/12 = .8333% per month), you get:

In[2]:= FutureValue[100, 20*12 , .10/12]

Out[2]= 75936.9

If your compounding and payments were at some other interval (quarterly
say), you would have to adjust accordingly. Or you could do a bit of
math to include that into your formula also.

To find the present value of an investment say, consisting of n equal
payments of D dollars, paying an interest rate of r per payment interval,
you would use:

In[3]:= PresentValue[D_, n_, r_]:= D(1 - (1 + r)^-n)/r

For example, to figure the monthly payment on a 4-year loan of $12,000
paying 12.9% interest rate compounded monthly, you would compute:

In[4]:= Solve[PresentValue[x, 4*12, .129/12] == 12000, x]

Out[4]= {{x -> 321.335}}

Hope this helps.

Paul Wellin
Academic and Business Liaison
Wolfram Research, Inc.
100 Trade Center Drive
Champaign, IL 61820

phone: 217-398-0700
fax:   217-398-0747
email: wellin at

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