Retirement Planning Basics: formula sheet

Key formulas

Future value of a current expense

Future expense = Current expense × (1 + inflation rate)^n

n is the number of years. Use it to show how inflation raises retirement cost. Inflation compounds, so it is not a simple addition.

Length of retirement phase

Retirement years = Life expectancy − Retirement age

Longer life expectancy with the same retirement age means more years to fund.

Defined benefit vs defined contribution

DB: employer promises the benefit. DC: employee bears the investment risk.

Shift from DB to DC moves risk to the individual.

Real return (approximate)

Real return ≈ Nominal return − Inflation rate

A return lower than inflation means a fall in purchasing power.

Phase sequence

Accumulation → Pre-retirement → Distribution

Distribution is also called decumulation. Do not confuse the order in options.

Risk capacity across phases

Accumulation: high | Pre-retirement: falling | Distribution: lowest

Capacity falls as earning years and recovery time shrink.

Typical asset mix direction

Equity share falls and debt/stable share rises as retirement nears

This is a direction, not a fixed rule. Exact mix depends on the client's profile and goals.

Core goal of each phase

Accumulate: grow corpus | Pre-retirement: protect and review | Distribution: generate sustainable income

Match the goal word in the question to the phase.

Capacity vs tolerance

Risk capacity = ability to bear loss; Risk tolerance = willingness to bear loss

If they conflict, the lower one should guide the recommendation.

Inflated expense at retirement

FV = PV × (1 + i)^n

PV is today's annual expense, i is inflation, n is years to retirement.

Real rate of return (exact)

r_real = [(1 + r) ÷ (1 + i)] − 1

r is post-retirement return, i is inflation. The shortcut r − i is only an approximation; use the exact form when options are close.

Corpus for level real annuity (payments at start of year)

Corpus = E × [(1 − (1 + r_real)^−N) ÷ r_real] × (1 + r_real)

E is first-year expense at retirement, N is retirement years. Use the annuity-due factor when the first withdrawal is made at retirement date.

Corpus (payments at end of year)

Corpus = E × [(1 − (1 + r_real)^−N) ÷ r_real] ÷ (1 + i)

Here E is the expense at retirement date; the first withdrawal is E × (1 + i) a year later, so divide by (1 + i). Check how the question defines the first withdrawal.

Retirement years

N = Life expectancy − Retirement age

Add any safety margin the question mentions.

Additional corpus required

Gap = Corpus needed − FV of existing investments

FV of existing investments = Amount × (1 + r)^n at the accumulation-phase return.

Annual saving to build the gap (end of year)

A = Gap × r ÷ [(1 + r)^n − 1]

r is the pre-retirement return. For monthly savings, use monthly rate and months.

Defined benefit pension

Pension is set by a formula (salary × service × factor)

Sponsor bears investment and longevity risk. Member knows the benefit in advance.

Defined contribution pension

Retirement corpus = contributions + investment returns

Member bears investment risk. Final benefit is not known in advance.

Income replacement ratio

Replacement ratio = Retirement income ÷ Pre-retirement income × 100

Shows how much of earlier income the sources replace.

Income from corpus

Annual income = Corpus × yield (or withdrawal rate)

Use for lump sums converted into income.

Annuity rate

Annual annuity = Purchase price × annuity rate

A guaranteed annuity rate fixes income; an annuity bought with a lump sum is generally not inflation-linked unless stated.

Real return (approximate)

Real return ≈ Nominal return − Inflation rate

Exact form: (1 + nominal) ÷ (1 + inflation) − 1. Use the approximate form only when the question allows it.

Future value of expense under inflation

Future expense = Current expense × (1 + inflation)^n

n is the number of years. Use it to show how inflation erodes fixed income.

Sequence risk rule

Same average return, different order = different ending corpus when withdrawals are made

With no withdrawals, order does not change the final value. The risk arises because of withdrawals.

Risk to mitigation match

Longevity → annuity; Inflation → equity and step-up; Sequence → safe bucket; Healthcare → health insurance; Interest rate → laddering

Memorise this pairing for MCQs.

Initial withdrawal amount

Year 1 withdrawal = Corpus × Withdrawal rate

Example: ₹1,00,00,000 × 4% = ₹4,00,000 in year one.

Inflation-adjusted withdrawal

Withdrawal in year n = Year 1 withdrawal × (1 + inflation)^(n − 1)

Used in the fixed-percentage-then-inflate method. Year 2 is year 1 × (1 + inflation).

Corpus needed for a target income

Corpus = Annual expense ÷ Withdrawal rate

Example: ₹6,00,000 ÷ 5% = ₹1,20,00,000. A lower rate needs a bigger corpus.

Sustainability test for SWP

Corpus lasts indefinitely only if withdrawals ≤ returns after inflation adjustment (roughly, real return ≥ withdrawal rate)

A guide, not a guarantee. Real return ≈ return − inflation.

Bucket sizing

Short-term bucket = Annual expense × number of years of cover

The number of years is a planning choice made by the adviser, not a fixed rule.

Retirement planning process order

Gather data → Set goals → Profile risk → Prepare plan → Obtain consent → Implement → Review

Exam questions often ask which step comes first or next. Data gathering and risk profiling come before any recommendation.

Risk profile rule

Risk the plan can take = lower of (risk capacity, risk tolerance)

If risk required is higher than this, revise goals or savings; do not raise risk beyond the client's limits.

Suitability principle

Advice must match the client's risk profile, goals, time horizon and financial situation

The reasons for the advice must be documented.

Adviser's duty basis

Client's interest first; disclose conflicts and fees; keep records; keep data confidential

These are duties under the SEBI (Investment Advisers) Regulations, 2013.

Quick revision

• Retirement planning aims to keep the lifestyle going after regular income stops.
• Longer life expectancy and rising costs increase the need for a larger corpus.
• Life-cycle stages change the balance between saving, growth and capital protection.
• Corpus estimation starts with the expected expense, adjusted for inflation up to retirement.
• Time to retirement and years in retirement both affect the corpus needed.
• Always check the client's existing resources before stating the shortfall.
• Retirement income can come from pensions, savings, investments and annuities.
• Inflation risk reduces what a fixed income can buy.
• Longevity risk is the risk of outliving the corpus.
• A withdrawal rate that is too high can exhaust the corpus early.
• The adviser must base advice on the client's profile, goals and suitability.
• Review the plan regularly because income, costs and markets change.

Common mistakes

• Treating longevity risk as the risk of dying early. Fix: Longevity risk is living longer than your savings last. Early death is a different risk, covered by life insurance.
• Adding inflation simply instead of compounding it. Fix: Use Current expense × (1 + rate)^n. For 6% over 2 years the factor is 1.1236, not 1.12.
• Saying a retired client should hold no equity at all. Fix: Retirement can last decades, so inflation risk remains. A measured growth portion usually stays, sized to the client's profile.
• Treating risk capacity and risk tolerance as the same. Fix: Capacity is ability to bear loss. Tolerance is willingness. Capacity depends on income, horizon and obligations.
• Using today's expense in the corpus calculation without inflating it Fix: Always do the FV step first. The corpus must fund expenses in retirement-date rupees.
• Using the nominal return and inflation separately and double counting Fix: Use the real rate with a level first withdrawal in retirement-date rupees, or model growing payments consistently.
• Calling NPS a defined benefit scheme Fix: NPS is defined contribution. The corpus depends on returns, so the member bears investment risk.
• Treating EPF and PPF as the same product Fix: EPF is linked to employment with employer contributions. PPF is open to individuals regardless of employment. Keep them separate.
• Treating sequence risk as the same as market risk. Fix: Market risk is any fall in value. Sequence risk needs withdrawals and bad returns early in retirement.
• Thinking sequence risk matters even with no withdrawals. Fix: Without withdrawals or contributions, the order of returns does not change the final value.

Exam tips

• Expect scenario questions that ask which factor is the main reason for planning. Read the clue words carefully.
• Remember that medical inflation is often higher than general inflation, so healthcare needs separate provision.
• Know the difference between defined benefit and defined contribution, and who bears the risk in each.
• For inflation numbers, compute the factor once and multiply. Check that the options are compounded, not simple.
• With 25% negative marking, skip only if you cannot remove at least two options.
• Most questions hand you clues. Identify the phase from salary status and years to retirement before reading the options.
• Watch for absolute words such as 'only', 'entire' and 'no equity'. They are often the trap in distribution-phase questions.
• Where options differ on capacity versus tolerance, choose the one that puts capacity first.