NISM Series X-B numericals are mostly multi-step: insurance needs analysis, retirement corpus and annuities, income-tax and capital-gains computations, estate division and product comparison. Take one of the two free 20-question numerical tests below (you need a free account), then use the formula sheet to fix whatever you got wrong. Every tax rate and limit a question needs is stated in the question itself. Scoring copies the real exam: +1 for a correct answer, −0.25 for a wrong one.
Two free 20-question tests, 40 different calculation questions in all: insurance needs, retirement corpus, capital gains and income tax, estate planning and product comparison. Every answer comes with the formula, the working and the common mistake when you finish.
NISM does not publish how many questions in each paper are numerical, so use this table as a guide to where calculations appear in the X-B syllabus. The last two columns show how many numerical questions BullWiser has written for each chapter (200 in the full bank, 40 of them in the two free tests).
| Chapter | What gets calculated | Full bank | Free tests |
|---|---|---|---|
| 1. Basics of Insurance | Capitalised income cover, human life value, needs-based cover, premium and loading | 20 | 2 |
| 2. Features of Life Insurance Products | ULIP units and charges, surrender and paid-up values, bonuses, plan CAGR | 15 | 2 |
| 3. Features of Non-Life Insurance Products | Average-clause claims, contribution, motor IDV and NCB, health co-pay and room rent | 12 | 2 |
| 4. Retirement Planning Basics | Inflated expenses, replacement ratio, retirement corpus, SIP needed, real return | 15 | 2 |
| 5. Retirement Products | Annuity corpus, PPF and EPF maturity, commutation, NPS lump sum and pension | 15 | 3 |
| 6. Miscellaneous Aspects of Retirement Planning | Bucket split, sequence-of-returns risk, safe-withdrawal-rate corpus, balance after withdrawals | 10 | 2 |
| 7. Concepts of Taxation | Slab tax with cess, regime choice, HRA, TDS, late-payment interest, advance tax | 12 | 2 |
| 8. Capital Gains | STCG and LTCG tax, grandfathered cost, loss set-off, reinvestment exemption, indexation | 15 | 2 |
| 9. Income from Other Sources | Taxable interest, gifts, dividend tax after TDS, family pension, lottery winnings | 8 | 3 |
| 10. Taxation of Debt Products | Post-tax yield of FDs, bonds and debt funds; taxable-equivalent yield | 8 | 3 |
| 11. Taxation of Equity Products | Equity gains with exemption, STT, buyback tax, switch tax, growth vs IDCW | 10 | 2 |
| 12. Taxation of Other Products | Speculative loss, REIT and insurance taxability, house property income, gold LTCG | 6 | 2 |
| 13. Tax Provisions for Special Cases | NRI TDS, clubbing of income, HUF saving, surcharge with marginal relief | 8 | 3 |
| 14. Basics of Estate Planning | Net and projected estate, liquidity shortfall, equalising insurance, will shares | 6 | 2 |
| 15. Tools for Estate Planning | Trust payout, trust corpus, probate fee, per stirpes shares, gift deed costs | 6 | 2 |
| 18. Risk Profiling for Investors | Stress loss, expected return, portfolio risk, equity limit, score-based allocation, rebalancing | 10 | 2 |
| 19. Comparison of Products across Categories | Post-tax and real returns, ULIP charge drag, endowment IRR, regular vs direct cost | 10 | 2 |
| 20. Case Studies | Integrated cases: estate, tax, retirement SIP, goals, insurance gap, risk-based gain | 14 | 2 |
Chapters 16, 17 are mostly theory, so they have no numerical set here.
Every formula below is used in the practice questions. Read the note column for conventions such as compounding period and sign.
| Measure | Formula | Note |
|---|---|---|
| Future value / present value | FV = PV × (1 + r)^n ; PV = FV ÷ (1 + r)^n | r and n must use the same period |
| CAGR and number of years | r = (FV/PV)^(1/n) − 1 ; n = ln(FV/PV) ÷ ln(1 + r) | |
| Effective annual yield | EAY = (1 + r/k)^k − 1 | k = compounding periods per year |
| Real return and purchasing power | Real = (1 + nominal) ÷ (1 + inflation) − 1 ; Real value = Amount ÷ (1 + inflation)^n | |
| SIP / annuity future value | FV = P × [(1 + i)^N − 1] ÷ i ; SIP needed = FV × i ÷ [(1 + i)^N − 1] | End-of-period investing; annuity-due = FV × (1 + i); i = periodic rate, N = periods |
| Present value of an annuity | PV = C × [1 − (1 + i)^−N] ÷ i ; Payment = PV × i ÷ [1 − (1 + i)^−N] | Perpetuity PV = C ÷ i |
| Measure | Formula | Note |
|---|---|---|
| Capitalised income cover | Cover = Annual income need ÷ Yield | |
| Human life value | HLV = (Income − Personal expenses) × [1 − (1 + r)^−n] ÷ r | For growing income use the growing-annuity formula above |
| Needs-based cover | Cover = PV(family expenses) + Liabilities + Goals − Existing assets − Existing cover | |
| Premium and loading | Annual premium = SA ÷ 1,000 × Rate ; Modal premium = Annual × Modal factor ; Gross = SA × Mortality rate × (1 + Loading %) | |
| Insurance pool surplus | Surplus = Lives × Premium − Lives × Mortality rate × Sum assured | |
| ULIP units and mortality charge | Units = (Premium − Allocation charge) ÷ NAV ; Mortality charge = (Death benefit − Fund value) ÷ 1,000 × Rate | |
| Traditional policy values | Paid-up SA = SA × Premiums paid ÷ Premiums payable ; Maturity = SA + Reversionary bonus + Final bonus ; GSV = SV% × (Premiums paid − First-year premium) | |
| Return-of-premium term vs term + invest | Excess = d × [(1 + r)^n − 1] ÷ r − Premiums returned | d = yearly premium difference |
| Measure | Formula | Note |
|---|---|---|
| Average clause and contribution | Claim = Loss × Sum insured ÷ Value at risk ; Loss = Claim × Value ÷ SI ; Insurer's share = Loss × Its SI ÷ Total SI | Claim cannot exceed the sum insured; with a deductible, subtract it after applying the ratio |
| Motor claim and no-claim bonus | IDV = Price × (1 − Depreciation %) ; Total-loss claim = IDV − Deductible − Salvage ; Premium = OD × (1 − NCB %) + TP | |
| Health claim with sub-limit and co-pay | Payable = [Days × Permitted rent + Other expenses × (Permitted rent ÷ Actual rent)] × (1 − Co-pay %) |
| Measure | Formula | Note |
|---|---|---|
| Inflated expense and replacement ratio | Future expense = Present × (1 + inflation)^n ; Replacement ratio = (Last pay − Savings − Expenses that cease) ÷ Last pay | |
| Corpus at a safe withdrawal rate | Corpus = Annual withdrawal ÷ SWR ; Income gap corpus = 12 × (Monthly expense − Other income) ÷ SWR | |
| Corpus with growing withdrawals | Corpus = W1 ÷ (r − g) × [1 − ((1 + g)/(1 + r))^m] ; W1 = Expense today × (1 + g)^n | |
| Annual saving to close a gap | Saving = (Target − Existing × (1 + r)^n) ÷ [((1 + r)^n − 1) ÷ r] | |
| PPF / EPF maturity | FV = Deposit × [((1 + r)^n − 1) ÷ r] ; PPF deposits at start of year × (1 + r) | |
| Annuity, commutation and NPS | Pension = Purchase price × Annuity rate ÷ 12 ; Lump sum = Corpus × (1 − Minimum annuity %) ; DB pension = min(Salary, Cap) × Service ÷ 70 |
| Measure | Formula | Note |
|---|---|---|
| Tax with cess | Total tax = Slab tax × 1.04 ; Effective rate = Tax ÷ Gross total income | |
| Marginal tax and capped deduction | Extra tax = Additional income × Slab rate × 1.04 ; Tax saved = min(Investment, Cap) × Rate × 1.04 | |
| HRA exemption | Least of: HRA received ; Rent − 10% of Basic ; 50% (metro) or 40% of Basic | |
| Late payment and advance tax | Interest = Shortfall × 1% × Months ; Instalment = Cumulative % due × (Tax − TDS) − Instalments paid | Part-month counts as a full month |
| Surcharge with marginal relief | Payable = min[Tax × 1.10, Tax on Rs. 50 lakh + Income above Rs. 50 lakh] × 1.04 | Applies where income just exceeds a surcharge threshold |
| Clubbing and TDS | Minor's income clubbed = Income − Rs. 1,500 per child ; NRO interest TDS = 30% × 1.04 ; NRI LTCG TDS = 12.5% × 1.04 |
| Measure | Formula | Note |
|---|---|---|
| Listed equity gains | STCG tax = 20% × Net STCG ; LTCG tax = 12.5% × (Net LTCG − Rs. 1,25,000) ; Grandfathered cost = max(Actual, min(FMV on 31-1-2018, Sale price)) | Net = after set-off of losses |
| Reinvestment exemption and indexed cost | Taxable gain = Gain × (1 − Invested ÷ Net consideration) ; Indexed cost = Cost × CII(sale) ÷ CII(purchase) | |
| Post-tax yield of debt products | Post-tax yield = Pre-tax yield × (1 − Slab rate × 1.04) ; Taxable-equivalent yield = Tax-free yield ÷ (1 − t) | |
| Let-out house property and units to redeem | Income = NAV × 70% − Loan interest ; Units to redeem = Exemption ÷ (Current NAV − Cost NAV) | NAV = Annual rent − Municipal taxes |
| Measure | Formula | Note |
|---|---|---|
| Estate value | Net estate = Assets − Liabilities ; Projected estate = Present × (1 + g)^n ; Liquidity shortfall = Settlement costs + Loans − Liquid assets | |
| Distribution of shares | Share = Estate × Heir's part ÷ Sum of parts ; Per stirpes: Grandchild = Branch share ÷ Grandchildren in that branch | |
| Trust payout and transfer costs | Payout = (Corpus × Yield − Corpus × Fee %) ÷ Beneficiaries ; Gift deed cost = Value × (Stamp duty % + Registration %) ; Probate fee = min(Rate × Estate, Cap) |
| Measure | Formula | Note |
|---|---|---|
| Portfolio return and risk | E(Rp) = Σ w × R ; σp = √[(w1σ1)² + (w2σ2)² + 2 w1 w2 ρ σ1 σ2] ; Sharpe = (Rp − Rf) ÷ σp | |
| Equity limit and allocation | Max equity % = Tolerable loss % ÷ Stress fall % ; Age rule: Equity % = 100 − Age ± Adjustment ; Rebalancing shift = Equity value − Target % × Total ; Required equity share = (r − Debt return) ÷ (Equity return − Debt return) | |
| Cost of higher expenses | Difference = P × [(1 + r)^n − (1 + r − e)^n] | e = extra annual expense ratio |
| FD vs debt fund and endowment IRR | FD = P × [1 + r(1 − t)]^n ; Debt fund = V − 12.5% × (V − P) ; Endowment IRR: solve P × [((1 + r)^n − 1) ÷ r] × (1 + r) = Maturity | Premiums at start of year |
Spoiler warning: if you want to test yourself first, take the tests above before reading the tables.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Human life value (level income) | Rs. 88.36 lakh | Net contribution = 15 - 6.00 = 9.00 lakh; annuity factor (8%, 20 yrs) = 9.8181; HLV = 9.00 x 9.8181 = Rs. 88.36 lakh. |
| 2 | ULIP units allotted | 6,750.00 | Invested = 1,20,000 x 0.90 = Rs. 1,08,000; units = Rs. 1,08,000 / 16.0 = 6,750.00. |
| 3 | Average clause - find the loss | Rs. 24.00 lakh | Loss = 12.00 x 60/30 = Rs. 24.00 lakh. |
| 4 | Expense inflated to retirement | Rs. 1,10,361 | 40,000 x 1.07^15 = Rs. 1,10,361. |
| 5 | NPS monthly pension from contributions | Rs. 35,437 | Corpus = Rs. 1,51,87,377; annuity purchase = Rs. 60,74,951; pension = Rs. 60,74,951 x 7% / 12 = Rs. 35,437. |
| 5 | Pension from a corpus over a fixed period | Rs. 93,036 | i = 0.0058, N = 240; 1,20,00,000 x 0.0058 / [1 - 0.2476] = Rs. 93,036. |
| 6 | Inflation-adjusted withdrawal in year k | Rs. 18.38 lakh | 10 x 1.07^9 = Rs. 18.38 lakh. |
| 7 | Marginal tax on additional income | Rs. 29,120 | Income moves from 13.2 to 14.6 lakh and stays in the 20% slab; 1,40,000 x 20% x 1.04 = Rs. 29,120. |
| 8 | Capital gain on mutual fund units under FIFO | Rs. 11,000 | Cost = 300 x 50 + 100 x 60 = Rs. 21,000; sale = 400 x 80 = Rs. 32,000; gain = Rs. 11,000. |
| 9 | TDS on bank interest above threshold | Rs. 4,600 | Bank A exceeds 40,000: 10% x 46,000 = Rs. 4,600; Bank B is below the threshold: nil. |
| 10 | Post-tax yield on a bank FD | 4.47% | Effective tax rate = 30% x 1.04 = 31.2%; 6.5% x (1 - 0.312) = 4.47%. |
| 10 | Total tax on a cumulative FD taxed yearly | Rs. 1,12,473 | Total interest = Rs. 3,60,489; tax = Rs. 3,60,489 x 30% x 1.04 = Rs. 1,12,473. |
| 11 | STT on a round-trip delivery trade | Rs. 100 | Buy = Rs. 40,000; sell = Rs. 60,000; STT = 0.1% x Rs. 1,00,000 = Rs. 100. |
| 12 | Deemed sale value on property (stamp duty value) | Rs. 3,75,000 | 110% x 80 = 88.0 lakh; 84 <= 88.0, so consideration = 80 lakh; gain = 30 lakh; tax = Rs. 3,75,000. |
| 13 | Clubbing of income from gifted funds (spouse) | Rs. 60,000 | 10,00,000 x 6% = Rs. 60,000. |
| 14 | Insurance to equalise inheritance | Rs. 160.0 lakh | Each child must get 200 lakh (equal to the son's business); daughter has 40; cover = 200 - 40 = Rs. 160.0 lakh. |
| 15 | Will with specific bequests and residue | Rs. 57.50 lakh | Residue = 120 - 15 - 20 = 85; Amit's residue = 85 x 2/4 = 42.50; total = Rs. 57.50 lakh. |
| 18 | Sharpe ratio | 0.83 | (16 - 6) / 12 = 0.83. |
| 19 | Effective annual yield | 6.14% | (1 + 0.01500)^4 - 1 = 6.14%. |
| 20 | Case: retirement SIP | Rs. 36,773 | Expenses at retirement = Rs. 19,24,281; corpus = Rs. 4,81,07,032; existing grows to Rs. 2,01,82,500; gap = Rs. 2,79,24,532; SIP = Rs. 36,773. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Human life value (growing income) | Rs. 97.26 lakh | = 9/(0.08 - 0.04) x [1 - (1.04/1.08)^15] = Rs. 97.26 lakh. |
| 2 | ULIP mortality charge on sum at risk | Rs. 3,000 | Death benefit = 15 lakh; SAR = 15 - 5 = 10 lakh; charge = 10,00,000/1000 x 3.0 = Rs. 3,000. |
| 3 | Average clause (underinsurance) - claim | Rs. 6.00 lakh | 10 x 60/100 = Rs. 6.00 lakh. |
| 4 | Real rate of return (Fisher) | 5.66% | 1.12/1.06 - 1 = 5.66%. |
| 5 | Pension commutation | Rs. 10,20,000 | (30,000/3) x 12 x 8.5 = Rs. 10,20,000. |
| 6 | Bucket strategy: equity bucket share | 76.0% | Buckets 1+2 = 6 x 6 = 36 lakh; equity = 150 - 36 = 114 lakh = 76.0%. |
| 7 | Choosing between two tax regimes | Rs. 23,400 | Regime A tax = Rs. 93,600; Regime B tax = Rs. 1,17,000; difference = Rs. 23,400. |
| 8 | Property LTCG with indexation | Rs. 10,60,000 | Indexed cost = 40x300/150 + 10x300/200 = 95.00 lakh; LTCG = 53.00 lakh; tax = Rs. 10,60,000. |
| 9 | Dividend income: tax payable after TDS | Rs. 8,640 | Tax = Rs. 80,000 x 20% x 1.04 = Rs. 16,640; less TDS Rs. 8,000 = Rs. 8,640. |
| 9 | Family pension taxable amount | Rs. 45,000 | Annual = Rs. 60,000; deduction = min(Rs. 20,000, 15,000) = Rs. 15,000; taxable = Rs. 45,000. |
| 10 | Tax on debt mutual fund gains at slab rate | Rs. 3,120 | Gain = 2,000 x 5.0 = Rs. 10,000; tax = Rs. 10,000 x 30% x 1.04 = Rs. 3,120. |
| 11 | Buyback proceeds taxed as deemed dividend | Rs. 83,200 | Proceeds = 1,000 x 400 = Rs. 4,00,000; tax = Rs. 4,00,000 x 20% x 1.04 = Rs. 83,200. |
| 12 | Speculative loss set-off | Rs. 1,20,000 | F&O profit = Rs. 4,00,000 is taxed in full: 30% x Rs. 4,00,000 = Rs. 1,20,000; the Rs. 80,000 loss is carried forward. |
| 13 | NRE vs NRO account interest | Rs. 18,720 | Rs. 60,000 x 30% x 1.04 = Rs. 18,720. |
| 13 | Surcharge with marginal relief | Rs. 14,56,000 | Tax = Rs. 13,65,000; with surcharge = Rs. 15,01,500; relief cap = Rs. 14,00,000; lower = Rs. 14,00,000; with cess = Rs. 14,56,000. |
| 14 | Net estate value | Rs. 162.0 lakh | Assets = 200; liabilities = 38; net = Rs. 162.0 lakh. |
| 15 | Trust payout after trustee fee | Rs. 3,00,000 | Income = Rs. 18,00,000; fee = Rs. 3,00,000; net = Rs. 15,00,000; / 5 = Rs. 3,00,000. |
| 18 | Stress-test loss | Rs. 17.00 lakh | Equity loss = 100.0 x 20% = 20.00; debt gain = 100.0 x 3% = 3.00; net = Rs. 17.00 lakh. |
| 19 | Purchasing power of a maturity amount | Rs. 11.17 lakh | 20 / 1.06^10 = Rs. 11.17 lakh. |
| 20 | Case: lump sum for two goals | Rs. 36.67 lakh | 20 x (1.05/1.10)^8 + 40 x (1.05/1.10)^12 = Rs. 36.67 lakh. |
Yes. Insurance needs analysis, retirement corpus, income-tax and capital-gains computations, estate division and product comparison all need calculations, and the case-based sets often combine several steps. NISM does not publish how many questions are numerical.
NISM's general candidate instructions say candidates may bring their own physical calculator, which must be silent and have no connectivity, and that rough sheets are provided by the invigilator. Confirm the rules in your registration or admit instructions before exam day.
The exam combines 90 MCQs of 1 mark and 6 case-study sets over 180 minutes, for 150 marks. The pass mark is 90 out of 150 (60%). Each wrong answer costs 25% of the question's marks. Unanswered questions score zero.
You get 1 mark for each correct answer and lose 0.25 for each wrong answer, the same 25% scheme as the exam for a 1-mark question. Skipped questions score zero.
Yes. Two 20-question numerical tests (40 solved questions) are free with a free BullWiser account, which takes a few seconds to create. The full bank of 200 numerical questions, served 25 at a time and favouring questions you have not seen, comes with BullWiser X-B mock access, a one-time payment of Rs 199 per series.
Yes. Every question in the two free tests shows the correct answer, the formula, the step-by-step working and the common mistake when you finish. The solutions are also published on this page, so you can read them without taking the test.
No. BullWiser prepared them from the standard formulas taught in the NISM workbook, and each has a worked explanation. Names of people, companies and funds are fictional. BullWiser is not affiliated with NISM.
Take the full-length X-B mock, read the X-B notes and question bank, or start with the chapters that have the most numericals: Basics of Insurance, Features of Life Insurance Products, Retirement Planning Basics.
Preparing for another paper? Numerical practice is also available for: