I've found this formula for the Future Value of a Growing Annuity: see here

I'm looking for a formula that will provide the future value similar to this formula, only where I can provide a fixed amount of growth every period. For instance, the growth would be $25 more every year rather than growing by 3% every year.

Anyone know the formula to accomplish this?

Preamble

The demonstration in the link states "The growth rate in this example would be the 5% increase per year", so although you mention substituting the growth rate of 3% I assume you mean that the 5% growth rate should be substituted by a fixed $25 increase. You can swap the figures as you please in the formula. The point is I'm fairly sure you want the growth rate substituted, not the interest rate. (In the example in the link 3% is the interest rate.)

Solution

I doubt you'll find a formula quoted so here is one derived, based on the example.

The formula on the link, with the example shown, can be found like this.

First, adding up the contribution from each year:-

2000*(1 + 0.05)^0*(1 + 0.03)^4 +
2000*(1 + 0.05)^1*(1 + 0.03)^3 +
2000*(1 + 0.05)^2*(1 + 0.03)^2 +
2000*(1 + 0.05)^3*(1 + 0.03)^1 +
2000*(1 + 0.05)^4*(1 + 0.03)^0 = 11700.75

This can be expressed as a sum like so:-

enter image description here

or simplified (using Mathematica ) to produce the formula:-

enter image description here

The calculation you require, with fixed $25 growth, is this:-

(2000 + 25*0)*(1 + 0.03)^4 +
(2000 + 25*1)*(1 + 0.03)^3 +
(2000 + 25*2)*(1 + 0.03)^2 +
(2000 + 25*3)*(1 + 0.03)^1 +
(2000 + 25*4)*(1 + 0.03)^0 = 10875.88

which can be expressed in this sum:-

enter image description here

This can be simplified in a couple of ways:-

enter image description here

So, taking the shorter version

FV = -((x - (1 + i)^n (i p + x) + i (p + n x))/i^2)

e.g.

x = 25
p = 2000
i = 0.03
n = 5

FV = 10875.88
  • What you've assumed in the preamble is correct. Thank you, this looks like a great solution that will work for me. – Nathan Francy Oct 16 '14 at 17:45
  • Jolly good. :-) – Chris Degnen Oct 16 '14 at 18:01

Your Answer

 
discard

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.