Growing Perpetuities

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A growing perpetuity is one whose payments increase at a certain rate forever. They can be valued by the following formula, where C1 is the payment during the upcoming payment period, r is the discount rate, and g is the growth rate:

PV_{Growing Perpetuity} =

Example:

Madeline and Thurgood Johnson wish to set up a trust fund for their grandson which will begin paying $5,000 next year. They wish to have the payments grow at 5% per year to keep pace with inflation. If the current discount rate is 8%, what should they pay for the perpetuity?

PV_{Growing Perpetuity} =