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:
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?
To start calculating, use financial functions by pressing APPS (third row second column),
ENTER, 1:FINANCE
For Time Value of Money, choose 1:TVM Solver, ENTER (last row and the very right column)
Proper compounding: Scroll down to P/Y and press: P/Y = 1,
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
PMT = Current Annual Salary/ (1+growth rate)
= (80,000/1.09)
=73,394.50
Second Step: enter the following
N = 40, number of payment/cash flows in the growing annuity.
I = 10.09 {(.20-.09)/(1+.09)}*100
PV = Unknown
PMT = -73,394.50 (80,000/1.09)
FV = 0
CPT PV = $711,731
