Question

Steve is Planning t retice in Couple of years he has estimated that his annl veguitemedt os Ha hi hig of the 1s year f retremeut wauld be tres, expects to live 22yeors afer refiremev How much ould he accumulased Clum Som) amaud in hs 851000 Per year. te er y ehvemed aslant at he beginirg pered is forced Assome inflation t be 2.5ソ and inuertmut return to be 7.25% еду. 1,068,32S Ir lul, 30 ARI, 210, 769 1. 118( 6o9

Answer 1

The amount to be accumulated is the PV of the annual
payments to be received.
The stream of payments is a growing annuity, whose PV is given by the
formula:
[P/(r-g)]*[1-(1+g/1+r)^n
Where
P = First end of year payment
r = Rate per period
g = growth rate = rate of inflation
n = number of periods
Substituting values we have
PV = 85000+((85000/(0.0725-0.025))*((1-(1.025/1.0725)^21)) =	$      12,10,764
Answer: $1,210,769 [Marginal difference from calculation is
due to difference in approximation]
Note:
The formula is for year end payments.
Since the payments occur in the beginning of each year, the
first payment would be 85000 and the formula is to be applied
from the 2nd payment onwards, that is for 21 years.