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Growing Annuity  

A growing annuity is a finite number of cash flows growing at a constant rate.   The formula for the present value of a growing annuity is:

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Problem:
Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the present value of his lifetime salary?

Clear time value of money memory: 2nd CLR TVM
Compounding should remain at P/Y = 1 (third row second column), ENTER (first row second column), down arrow (first row fourth column), C/Y = 1.

First step: find out I and PMT

I = {(interest rate-growth rate)/(1+growth rate)}*100
  = {(.20-.09)/(1+.09)}*100
  =10.09
Press STO, 1 to store the number
PMT = Current Annual Salary/ (1+growth rate)
         = (80,000/1.09)
         =73,394.50
Press STO, 2 to store the number

Second Step: enter the following

N = 40, number of payment/cash flows in the growing annuity.
I = press RCL, 1 to recall the number we saved
PV = Unknown
PMT = RCL, 2 to recall the number
FV = 0
CPT PV = $711,731 

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Last Updated on 1 May 2002, e-mail any comments to: robert.balik@wmich.edu