The document discusses how inflation impacts retirement planning and presents a mathematical model to determine the necessary capital accumulation and expenses to maintain a desired lifestyle after retirement given expected rates of return, income, inflation. It applies the model to an example scenario of an IITK professor planning for retirement in 15 years and finds their initial savings and expense estimates would be insufficient unless lifestyle is reduced by 20% during retirement. The model can be used annually to help individuals better plan expenses that account for inflation.

1. Effect of Inflation on Retirement
Planning
Submitted By:
Pranjal Jaiswal (11515)

2. Introduction
• Inflation is when you pay hundred rupees for a
fifty rupees haircut you used to get for twenty
rupees when you had hair.
• The rate at which the general level of prices for
goods and services is rising, and, subsequently,
purchasing power is falling.
• Inflation means just about everything costs more,
maybe a bit or a lot more.

3. Role of Inflation in our lives
• With inflation rising and wages remaining low, the standard of living
in India is also likely to take a hit.
• Inflation usually hurts your buying power

4. Problem Statement
How should you plan your expenses when factoring in
inflation so that life after retirement is financially stable?

5. System Characterization
System An individual who has to plan his personal finances
Company, where he works and gets an income I(n)
Market, where he spends his money E(n)
Bank which gives a return on his capital
Deterministic/
Stochastic
This is deterministic model as no random variables are used.
Dynamic/Static As time factor is involved in the model so the model is dynamic
Closed /Open Model is closed system as it doesn’t interact with the
surroundings

6. Parameters S = capital at start of calculation
i = after-tax return on capital
Variables Sn = capital accumulation at year n
I(n) = after-tax income from all other
sources, function of n
E(n) = living expense as a function of n

7. Mathematical Formulation
Differential equation states that the change in capital with
time equals the after-tax income minus the expense,
(1)
Solution to the differential equation is given by,
(2)

8. •If living expense rises at the continuously
compounded rate if due to inflation, then the expense
function is given by
(3)
E0 is the initial living expense at n = 0
•The income function often consists of a fixed part and
a part partially or wholly indexed to inflation. Hence,
the income function may be expressed as
(4)

9. Substituting equations (3) and (4) into (2), we get:
(5)
Let iv = ia = if = i, then:
(6)

10. A Numerical Example Of Planning
• There is an IITK professor’s family of 2014, 15 years before
expected retirement in 2029, he wish to plan for financial
survival at least as long as their probable lifetimes. It is
assumed that the average time of survival after retirement is
20 years.
• Inserting the above rates in (5) with n = 15, and
assuming no fixed income (F = 0), gives the 2029
accumulation of capital as:
(7) S15 = 2.85So + 54.1(Ao-Eo)

11. • After retirement, the survival condition is found by using n
= 20 and equating (5) to zero. This gives
(8) S'+ 10.8F' + 27.4 ( Ao
’- Eo
’ )= 0
• We assume: ia= if = 0.10
iv = 0.07
• To further simplify, let the 2029 fixed income, F', be an
after-tax pension equal to half of the 2029 after-tax salary.
Then, from (4),

12. Ao’ (Social Security) = E0’/3.
Combining (7) and (8) with these conditions gives the final
survival condition
(9) Eo = 0.053So + 1.45Ao - 0.34E’o
If the planner wishes to continue the 2014 life style into
retirement, then (3) shows that
Eo'= Eo e1.5
= 4.48Eo
Eo = 0.021 So + 0.58Ao
Ao = INR 15,00,000 (After tax salary)
So = INR 40,00,000 (Accumulation at the end of 2014)
Eo = INR 9,54,000 (the family may adopt a life style
equivalent to in 2014 rupees)

13. From (7) S15 = INR 4,09,00,000
From (8) S'+ 10.8F' = INR 7,71,88,000
27.4(A’o-E’o) = - INR 7,80,70,272
Therefore, S'+ 10.8F‘ + 27.4(A’o-E’o) = - INR 8,82,272
Hence, their capital accumulation will be insufficient to permit
continuation of the life style into retirement.
An alternative is to plan to reduce retirement life style to
80% of that during earning years
From (9): E0 = INR 10,75,923.121
S15 = INR 3,43,42,559.14

14. from (8), we find that,
S'+ 10.8F' = INR 7,06,30,559.14
27.4( Ao
’ - Eo
’ ) = 27.4 x 2/3 x 4.48 x 0.8 x Eo
= INR 7,04,38,247.97
Therefore, S'+ 10.8F‘ + 27.4(A’o-E’o)= INR 1,92,311.17
Thus, it shows that they may then increase 2014 living
expense to Eo = INR 10,75,923.121 . Without planning, most
professionals will be tempted to live more expensively than
the life style suggested by the model. If used annually as
assumptions change, the model greatly reduces the
likelihood of financial failure after retirement.

15. • Current Inflation rate: 8.15% (in India)
So, this model can be applied with the appropriate values
of different variables and parameters and can be used to
estimate the expenses through which we can manage
after our retirement.
Future Modifications
• Monthly inflation rates may be considered instead on
annually and model maybe used on a monthly basis.

16. Conclusion
• To ensure that your savings will have the necessary
purchasing power, your savings will need to outpace
inflation
• To prevent financial collapse the model should be used many
years before retirement and re-applied annually
• Amount you save will need to increase by the same
percentage of inflation every year to ensure purchasing
power parity

17. References
• E. W. HEROLD, How inflation affects your retirement dollar,
IEEE Spectrum, 16 (Sept. 1979), pp. 58-60
• Inflation Mathematics for Professionals,
Edward W. Herold