Determining the principal amount required to provide an
ordinary annuity, adjusted for inflation, for a finite period of time.
Question
What sum today will be sufficient to capitalize a trust designed to provide an ordinary annuity beginning with $3,000 per month and adjusted for inflation each month over 15 years, if cash in the trust fund can be invested to net 7.5% p.a. and inflation averages 2.5% p.a.?
The amount necessary to capitalize this fund is
$378,836.39.
The inflation-adjusted rate (IAR) in this problem is 0.4158% per month. (12.075/12.025)-1
x100)
n i
PV
PMT
FV
180 0.4158 ?
-3,000
0
Solving
379,625.63
However, when the IAR is used to determine the Present Value of an ordinary annuity
payment (EOP) the result is always overstated by a factor = (1 + inflation rate).
To obtain the correct answer, divide the calculator's answer by (1 + inflation rate), or:
PV = $379,625.63 / (1 + (.025/12)) = $378,836.39.
In problems in which the amount of the trust (the present value) is given and an ordinary
annuity (a payment), adjusted for inflation, is sought, the calculator will always deliver
a PMT which is understated by (1 + inflation rate). To correct, multiply the calculator's
payment answer by (1 + inflation rate).
This discrepancy does not occur when dealing with an annuity due or with problems involving Future Values.
The cause of the discrepancy is that the calculator multiplies every ordinary
annuity payment by (1+ inflation rate) and then discounts it by (1 + nominal rate). But in
an ordinary annuity situation, the first payment, occurring at the end of the first period,
ought not be inflated. It is stipulated.
In dealing with an annuity-due, the calculator neither inflates nor discounts the first
payment, and therefore this error is not encountered.