this is a sum of payments in a perpetuity. typically, the formula is C=r/g. in this case, C is replaced with A, and i1 and i2 are the different values for g

Derive an expression for present value of this perpetuity of cash flows. The initial payment is realized at p=1 as A. Until year 3, payments grow with a rate of i1. From p=4 onward, payments grow at a rate of i2. Discount rate is period p 1 2 Payment A A(1+i1) 3 A(1+i1)^2 4 A(1+i1)^2 (1+i2) 5 A(1+i1)^2 (1+2)^2