NISM Series XVII Formula Sheet
Ten formulas, what each one is for, and a worked example.
Retirement planning comes down to one question: how big must the corpus be, and how much must you save to build it? Series XVII tests each step of that calculation.
These ten formulas follow the order an adviser works in, with a full worked corpus example.
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The 10 Formulas
1
Formula
Expense at retirement
Expression
Current expense × (1 + Inflation)ⁿ
Use it for
Inflating today's annual expense to the retirement year.
2
Formula
Real rate of return
Expression
(1 + Nominal return) ÷ (1 + Inflation) − 1
Use it for
The return that grows a corpus faster than its withdrawals rise.
3
Formula
Corpus needed (withdrawals at start of year)
Expression
E × [1 − (1 + r)⁻ⁿ] ÷ r × (1 + r)
Use it for
Lump sum that funds inflation-linked expenses for n years.
4
Formula
Corpus needed (perpetuity)
Expression
E ÷ r
Use it for
Corpus that never runs out at a real return r.
5
Formula
Future value of savings so far
Expression
Current savings × (1 + r)ⁿ
Use it for
What existing investments will be worth at retirement.
6
Formula
Shortfall
Expression
Corpus needed − FV of existing savings
Use it for
The gap that new saving must fill.
7
Formula
Annual saving needed
Expression
Shortfall × r ÷ [(1 + r)ⁿ − 1]
Use it for
Yearly investment to close the gap by retirement.
8
Formula
Annuity income
Expression
Annuity purchase price × Annuity rate
Use it for
Pension from an annuity bought with part of the corpus.
9
Formula
Withdrawal rate
Expression
First-year withdrawal ÷ Corpus × 100
Use it for
Checking whether withdrawals are sustainable.
10
Formula
Replacement ratio
Expression
Retirement income ÷ Pre-retirement income × 100
Use it for
How much of working income the plan replaces.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Expense at retirement | Current expense × (1 + Inflation)ⁿ | Inflating today's annual expense to the retirement year. |
| 2 | Real rate of return | (1 + Nominal return) ÷ (1 + Inflation) − 1 | The return that grows a corpus faster than its withdrawals rise. |
| 3 | Corpus needed (withdrawals at start of year) | E × [1 − (1 + r)⁻ⁿ] ÷ r × (1 + r) | Lump sum that funds inflation-linked expenses for n years. |
| 4 | Corpus needed (perpetuity) | E ÷ r | Corpus that never runs out at a real return r. |
| 5 | Future value of savings so far | Current savings × (1 + r)ⁿ | What existing investments will be worth at retirement. |
| 6 | Shortfall | Corpus needed − FV of existing savings | The gap that new saving must fill. |
| 7 | Annual saving needed | Shortfall × r ÷ [(1 + r)ⁿ − 1] | Yearly investment to close the gap by retirement. |
| 8 | Annuity income | Annuity purchase price × Annuity rate | Pension from an annuity bought with part of the corpus. |
| 9 | Withdrawal rate | First-year withdrawal ÷ Corpus × 100 | Checking whether withdrawals are sustainable. |
| 10 | Replacement ratio | Retirement income ÷ Pre-retirement income × 100 | How much of working income the plan replaces. |
What the Symbols Mean
- E
- Annual expense in the first year of retirement.
- r
- Real (inflation-adjusted) rate of return during retirement.
- n
- Years to retirement, or years in retirement, depending on the formula.
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Worked Example: Retirement Corpus
Annual expenses are ₹6,00,000 today, with retirement 20 years away and 6% inflation. Retirement is planned to last 25 years at a real return of 1.5%.
- 1
Expense in the first year of retirement
6,00,000 × (1.06)²⁰ ≈ ₹19,24,000.
- 2
Annuity factor for 25 years at 1.5%, paid in advance
[1 − (1.015)⁻²⁵] ÷ 0.015 × 1.015 ≈ 21.03.
- 3
Corpus
19,24,000 × 21.03 ≈ ₹4.05 crore needed on the retirement date.
Use the Real Rate After Retirement
During retirement, withdrawals rise with inflation. Discounting at the real rate handles that in one step. Using the nominal rate understates the corpus badly.
FAQs
Why use the real rate rather than nominal?expand_more
Because expenses grow with inflation. The real rate measures how fast the corpus grows relative to those expenses.
Why multiply by (1 + r) in the corpus formula?expand_more
Retirees usually withdraw at the start of each year. That's an annuity due, which is worth (1 + r) times an ordinary annuity.
How much of the NPS corpus must buy an annuity?expand_more
For non-government subscribers, at least 20% at normal exit since PFRDA's December 2025 amendment (it was 40% before), and small corpuses can be withdrawn in full. Check the current rules, as PFRDA revises them.
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