I complete forgot the formula to solve this sort of equations ... can someone please put me on the right track.

Key:

  • Saving rate = Q
  • Annual salary=W
  • Rate of salary increases per year (in percentage) = Z
  • Initial year = A
  • Maximum number of years = N
  • Total savings per year= Gx
  • Total savings: H


  • Formula: G=W*[Power(1+Z),(N-A)]*Q

If A=1 W=40000 Q=.3 Z=.02
Then in the first year N= 1 thus G0= 12000
Then in the second year N=2 thus G1= 12240
Total savings from first year to second year: H= G0+G1

Problem: Derive the formula to determine the total savings from the first year to the "N" year? [where N is a natural positive whole number]

Correct me if I'm wrong:

  • This is what it must look like:

H=G0+G1+G2+G3+........GN
= W*Q*( 1+ [Power(1+Z),2] +[Power(1+Z),3]+.....+ [Power(1+Z),(N-A)])
But how do we reduce this to a single formula.