# How to calculate the growth rate of a growing annuity? [closed]

I have a question that seems basic but has given me fits. If I have the following known variables, how do I solve for the growth rate?

Known variables:

• initial payment
• outstanding balance
• number of periods

I need to solve for growth rate of payment where the cumulative value equals the outstanding balance... assume a zero discount rate (i.e. interest free)

Example:

If I have a goal to save 20k in cash, and my initial saving per period is 1k, what is the growth rate per period required to reach 20k if I only make 17 deposits?

• Unfortunately, this is a basic finance question and this site is dedicated to professionals/academics in quantitative finance. You can try your luck in forums dedicated to the CFA curriculum, for example. – SRKX Jan 23 '15 at 9:37
• The summation for an annuity-due is s = Σ a (1 + r)^k for k = 1 to n which, by induction, has the closed-form s = (a (1 + r) (-1 + (1 + r)^n))/r. Solving for r where 20000 = (1000 (1 + r) (-1 + (1 + r)^17))/r finds r = 0.0177995 – Chris Degnen Jan 27 '15 at 9:45