NISM Series X-A Formula Sheet
Ten formulas, what each one is for, and a worked example.
Level 1 of the investment adviser exam is a financial planning exam, and financial planning runs on time value of money. These ten formulas let you project a goal, find the saving needed and check a return after inflation and tax.
A worked goal-cost example follows the table.
The 10 Formulas
1
Formula
Future value (lump sum)
Expression
FV = PV × (1 + r)ⁿ
Use it for
What an investment grows to.
2
Formula
Present value (lump sum)
Expression
PV = FV ÷ (1 + r)ⁿ
Use it for
What a future amount is worth today.
3
Formula
Future cost of a goal
Expression
Today's cost × (1 + Inflation)ⁿ
Use it for
Inflating a goal, such as education, to the year it's needed.
4
Formula
Future value of a SIP
Expression
FV = A × [(1 + r)ⁿ − 1] ÷ r
Use it for
Corpus built by regular saving at the end of each period.
5
Formula
Monthly saving needed
Expression
A = FV × r ÷ [(1 + r)ⁿ − 1]
Use it for
SIP needed to reach a goal.
6
Formula
Present value of an annuity
Expression
PV = A × [1 − (1 + r)⁻ⁿ] ÷ r
Use it for
Value of a series of payments, such as a loan or an income.
7
Formula
Real rate of return
Expression
(1 + Nominal) ÷ (1 + Inflation) − 1
Use it for
Return after inflation.
8
Formula
Post-tax return
Expression
Pre-tax return × (1 − Tax rate)
Use it for
Comparing taxable and tax-free options.
9
Formula
CAGR
Expression
(Ending value ÷ Beginning value)^(1/n) − 1
Use it for
Annualised growth between two values.
10
Formula
Rule of 72
Expression
Years to double ≈ 72 ÷ Interest rate (%)
Use it for
Quick estimate of doubling time.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Future value (lump sum) | FV = PV × (1 + r)ⁿ | What an investment grows to. |
| 2 | Present value (lump sum) | PV = FV ÷ (1 + r)ⁿ | What a future amount is worth today. |
| 3 | Future cost of a goal | Today's cost × (1 + Inflation)ⁿ | Inflating a goal, such as education, to the year it's needed. |
| 4 | Future value of a SIP | FV = A × [(1 + r)ⁿ − 1] ÷ r | Corpus built by regular saving at the end of each period. |
| 5 | Monthly saving needed | A = FV × r ÷ [(1 + r)ⁿ − 1] | SIP needed to reach a goal. |
| 6 | Present value of an annuity | PV = A × [1 − (1 + r)⁻ⁿ] ÷ r | Value of a series of payments, such as a loan or an income. |
| 7 | Real rate of return | (1 + Nominal) ÷ (1 + Inflation) − 1 | Return after inflation. |
| 8 | Post-tax return | Pre-tax return × (1 − Tax rate) | Comparing taxable and tax-free options. |
| 9 | CAGR | (Ending value ÷ Beginning value)^(1/n) − 1 | Annualised growth between two values. |
| 10 | Rule of 72 | Years to double ≈ 72 ÷ Interest rate (%) | Quick estimate of doubling time. |
Worked Example: Future Cost of a Goal
A goal costs ₹10,00,000 today and is 10 years away. Inflation is 6% a year.
- 1
Inflation factor
(1.06)¹⁰ ≈ 1.7908.
- 2
Future cost
10,00,000 × 1.7908 ≈ ₹17,90,800.
- 3
Next step
Use the "monthly saving needed" formula on this amount to find the SIP required.
Free account, this exam preselected.
Beginning or End of the Period?
The SIP and annuity formulas here assume payments at the end of each period. If the question says payments start today, multiply the result by (1 + r).
FAQs
Is the real return just nominal minus inflation?expand_more
That's a close approximation. The exact real return is (1 + nominal) ÷ (1 + inflation) − 1, which is slightly lower.
Should I use monthly or annual rates for a SIP?expand_more
Monthly. Divide the annual rate by 12 and count the periods in months.
How accurate is the rule of 72?expand_more
It's close for rates between about 6% and 10%, which is why it's useful for quick checks.
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