NISM Series X-A puts numbers into most of its chapters: time value of money, loans, stock and bond valuation, derivatives, mutual funds, portfolio theory and performance measurement, and its case-based sets often chain several calculations together. 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. 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: time value of money, EMI and loans, stock valuation, bonds, portfolio theory and performance measures. 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-A 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. Introduction to Personal Financial Planning | Human life value, needs-based insurance cover, inflation-adjusted expenses | 3 | 2 |
| 2. Time Value of Money | FV, PV, annuities, perpetuities, EAR, SIP goals, real rate | 20 | 3 |
| 3. Cash Flow Management and Budgeting | Savings, liquidity, solvency and debt-service ratios, net worth, emergency fund | 12 | 2 |
| 4. Debt Management and Loans | EMI, outstanding principal, FOIR, loan eligibility, prepayment, credit-card cost | 15 | 3 |
| 5. Introduction to Indian Financial Markets | Free-float market cap, index level, CRR/SLR, repo interest, market cap-to-GDP | 5 | 2 |
| 7. Introduction to Investments | HPR, CAGR, geometric mean, expected return and SD, post-tax and real returns | 12 | 2 |
| 8. Investing in Stocks | P/E, P/B, dividend yield, DuPont, DDM, EV/EBITDA, rights and bonus issues | 20 | 3 |
| 9. Investing in Fixed Income Securities | Bond price, current yield, YTM, duration, dirty price, T-bill yield, forward rates | 20 | 2 |
| 10. Understanding Derivatives | Futures fair value, option payoffs, put-call parity, hedge ratio, margins | 12 | 3 |
| 11. Mutual Fund | NAV, exit load, SIP average cost, TER impact, turnover, tax on redemption | 10 | 2 |
| 12. Portfolio Manager | PMS fixed fee, hurdle and high-water-mark performance fee, net return | 5 | 2 |
| 13. Overview of Alternative Investment Funds | AIF carry with hurdle, drawdowns, management fee, DPI and TVPI | 5 | 2 |
| 14. Introduction to Modern Portfolio Theory | Portfolio return and SD, beta, CAPM, Sharpe, Treynor, Jensen, CML | 20 | 4 |
| 15. Portfolio Construction Process | Asset allocation amounts, rebalancing, required return, corpus, risk budget | 12 | 2 |
| 16. Portfolio Performance Measurement and Evaluation | TWR, IRR, tracking error, information ratio, M-squared, Sortino, drawdown, attribution | 20 | 2 |
| 17. Operational Aspects of Investment Management | Net settlement, custody fees, contract note charges, impact cost | 5 | 2 |
| 18. Key Regulations | Compliance arithmetic against stated limits: exposure, fee cap, expense slabs | 4 | 2 |
Chapters 6, 19, 20 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 |
| Effective annual rate | EAR = (1 + r/m)^m − 1 | m = compounding periods per year |
| Real rate (Fisher) | Real = (1 + nominal) ÷ (1 + inflation) − 1 | Subtracting inflation is only an approximation |
| CAGR, rate and number of periods | r = (FV/PV)^(1/n) − 1 ; n = ln(FV/PV) ÷ ln(1 + r) | |
| Future value of an annuity (SIP) | FV = P × [(1 + i)^N − 1] ÷ i ; annuity-due = FV × (1 + i) | Sinking-fund payment = FV × i ÷ [(1 + i)^N − 1]; i = periodic rate, N = number of periods |
| Present value of annuity and perpetuity | PV = C × [1 − (1 + r)^−n] ÷ r ; annuity-due = PV × (1 + r) ; perpetuity = C ÷ r | |
| Growing annuity | PV = C1 ÷ (r − g) × [1 − ((1 + g)/(1 + r))^n] | C1 is the first payment, one period from now |
| Measure | Formula | Note |
|---|---|---|
| Savings ratio | (Income − Expenses − EMIs) ÷ Income | Use the same income base as stated in the question |
| Liquidity and solvency ratios | Liquidity = Liquid assets ÷ Monthly expenses ; Solvency = Net worth ÷ Total assets | Net worth = Total assets − Total liabilities |
| Debt service ratio / FOIR | Total EMIs ÷ Income | Gross income for debt service ratio; net income for FOIR as defined by the lender |
| EMI and outstanding loan | EMI = P × i × (1 + i)^N ÷ [(1 + i)^N − 1] ; Outstanding = EMI × [1 − (1 + i)^−(N−k)] ÷ i | i = annual rate ÷ 12, N = months, k = EMIs paid |
| Part-prepayment, same tenure | New EMI = EMI × (Outstanding − Prepayment) ÷ Outstanding | |
| Human life value and needs cover | HLV = PV of (Income − Personal expenses) ; Additional cover = Needs − (Liquid assets + Existing cover) |
| Measure | Formula | Note |
|---|---|---|
| Holding period and annualised return | HPR = (P1 − P0 + D) ÷ P0 ; Annualised = (1 + HPR)^(365/days) − 1 | |
| Geometric mean return | [(1 + r1)(1 + r2)…(1 + rn)]^(1/n) − 1 | |
| Expected return and SD (scenarios) | E(R) = Σ p × R ; SD = √[Σ p × (R − E(R))²] | |
| Valuation multiples | P/E = Price ÷ EPS ; P/B = Price ÷ BVPS ; PEG = P/E ÷ growth (%) ; Dividend yield = DPS ÷ Price ; EV/EBITDA = (Mkt cap + Debt − Cash) ÷ EBITDA | |
| ROE, growth and dividend discount model | ROE = Margin × Turnover × Leverage ; g = ROE × Retention ; P0 = D1 ÷ (k − g), D1 = D0 × (1 + g) | Two-stage: discount high-growth dividends, then add the discounted terminal value |
| Rights and bonus issues | TERP = (Held × Cum price + New × Issue price) ÷ (Held + New) ; Ex-bonus price = Cum price ÷ (1 + bonus ratio) |
| Measure | Formula | Note |
|---|---|---|
| Bond price | P = Σ C ÷ (1 + y)^t + Face ÷ (1 + y)^n ; zero-coupon P = Face ÷ (1 + y)^n | |
| Current yield and approximate YTM | CY = Annual coupon ÷ Price ; YTM ≈ [C + (F − P)/n] ÷ [(F + P)/2] | |
| Duration and price change | Mac. duration = Σ t × PV(CFt) ÷ Price ; ModD = MacD ÷ (1 + y) ; %ΔP ≈ −ModD × Δy | Portfolio duration is the value-weighted average |
| Dirty price and T-bill yield | Dirty = Clean + Face × Coupon × days/365 ; T-bill yield = (Face − Price) ÷ Price × 365/days | |
| Forward rate and tax-equivalent yield | f = (1 + s2)² ÷ (1 + s1) − 1 ; Taxable-equivalent = Tax-free yield ÷ (1 − t) |
| Measure | Formula | Note |
|---|---|---|
| Futures fair value | F = S × (1 + r × days/365) − Dividends ; continuous: F = S × e^(rT) | State the convention used in the question |
| Put-call parity | C − P = S − K ÷ (1 + r)^T | European options, no dividends |
| Option P&L and hedge ratio | Long call = max(S − K, 0) − Premium ; Short put = Premium − max(K − S, 0) ; Contracts = Beta × Value ÷ (Futures price × Lot) |
| Measure | Formula | Note |
|---|---|---|
| NAV, TER and turnover | NAV = (Assets − Liabilities) ÷ Units ; TER = Expenses ÷ Average net assets ; Turnover = min(Purchases, Sales) ÷ Average AUM | |
| PMS fees | Fee = Fixed % × Capital + Perf. % × max(Return − Hurdle, 0) × Capital ; High-water mark fee = Perf. % × max(Value − HWM, 0) | |
| AIF carry and multiples | Carry = Carry % × max(Proceeds − Capital × (1 + h)^n, 0) ; DPI = Distributions ÷ Paid-in ; TVPI = (Distributions + Residual value) ÷ Paid-in |
| Measure | Formula | Note |
|---|---|---|
| Portfolio return and risk | E(Rp) = Σ w × R ; σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2 | |
| Covariance and beta | Cov = ρ × σ1 × σ2 ; β = Cov(i, m) ÷ σm² = ρ × σi ÷ σm | |
| CAPM and capital market line | E(R) = Rf + β × (Rm − Rf) ; CML: E(Rp) = Rf + [(Rm − Rf) ÷ σm] × σp | |
| Risk-adjusted performance | Sharpe = (Rp − Rf) ÷ σp ; Treynor = (Rp − Rf) ÷ β ; Jensen α = Rp − [Rf + β(Rm − Rf)] | |
| Systematic risk and minimum variance | Systematic share = β²σm² ÷ σ² ; w1(min var) = (σ2² − Cov) ÷ (σ1² + σ2² − 2 Cov) |
| Measure | Formula | Note |
|---|---|---|
| Time-weighted and money-weighted return | TWR = Π(1 + R_sub-period) − 1 ; IRR: solve Σ CFt ÷ (1 + r)^t = 0 | TWR removes the effect of external cash flows |
| Active-risk measures | Tracking error = SD of (Rp − Rb) ; IR = Active return ÷ TE ; M² = Rf + Sharpe_p × σm − Rm ; Sortino = (Rp − MAR) ÷ Downside deviation | |
| Capture, drawdown and attribution | Up-capture = Fund up-market return ÷ Benchmark up-market return ; Max drawdown = min(NAV ÷ Running peak − 1) ; Allocation = (wp − wb)(Rb,sector − Rb,total) | |
| Portfolio construction and trading | Rebalancing trade = Current value − Target % × Total ; Corpus = Annual expense ÷ Withdrawal rate ; Impact cost = (Avg price − Mid price) ÷ Mid price |
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 (income method) | Rs. 1,22,37,434 | Annual surplus = 18,00,000 x 0.70 = 12,60,000; PV = 12,60,000 x [1 - 1.06^-15]/0.06 = Rs. 1,22,37,434. |
| 2 | PV of a growing annuity | Rs. 15,47,753 | 2,00,000 / (0.10 - 0.06) x [1 - (1.06/1.10)^10] = Rs. 15,47,753. |
| 2 | PV of a lump sum | Rs. 2,28,869 | 3,00,000 / (1 + 0.07)^4 = Rs. 2,28,869. |
| 3 | Months to build a target fund | 12 months | (3,00,000 - 60,000) / 20,000 = 12.00 -> 12 months. |
| 4 | Effective annual cost of card interest | 34.49% | (1 + 0.0250)^12 - 1 = 34.49%. |
| 4 | FOIR / debt-to-income ratio | 18.00% | (12,000 + 15,000) / 1,50,000 = 18.00%. |
| 5 | CRR and SLR lendable funds | Rs. 62,000 crore | 80,000 x (1 - 0.225) = Rs. 62,000 crore. |
| 7 | CAGR from start and end value | 10.00% | (2.1436)^(1/8) - 1 = 10.00%. |
| 8 | Implied required return (Gordon) | 11.67% | 10/150 + 5% = 11.67%. |
| 9 | Treasury bill yield | 5.99% | (2.90/97.10) x 365/182 = 5.99%. |
| 10 | Bull call spread | Rs. 1,700 | Net debit = 12 - 9 = 3; max profit = (20 - 3) x 100 = Rs. 1,700; break-even = 400 + 3 = 403. |
| 11 | Fund return with IDCW | 15.00% | (22 - 20 + 1) / 20 = 15.00%. |
| 12 | PMS net return to the client | 13.90% | 18 - 2.5 - 0.20 x (18 - 10) = 13.90%. |
| 13 | AIF management fee on commitment | Rs. 1.250 crore | 10 x 0.025 x 5 = Rs. 1.250 crore. |
| 14 | Portfolio beta | 0.960 | 0.40 x 1.2 + 0.40 x 0.9 + 0.20 x 0.6 = 0.960. |
| 14 | Treynor ratio | 11.25 | (16 - 7) / 0.8 = 11.25. |
| 15 | Equity weight drift after market moves | 75.50% | Equity = 98.00; debt = 31.80; weight = 75.50%. |
| 16 | Choosing between two funds: Sharpe vs Treynor (caselet) | Sharpe: Fund A; Treynor: Fund B | Sharpe: A = 0.750, B = 0.389; Treynor: A = 6.43, B = 7.00. |
| 17 | Impact cost | 0.058% | Average price = (500 x 400.40 + 100 x 400.60) / 600 = 400.4333; ideal = 400.200; impact = 0.058%. |
| 18 | Single-issuer exposure limit (stated) | Rs. 26.0 crore | 8% x 1200 = 96.0; less 70 = Rs. 26.0 crore. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Needs-based life insurance cover | Rs. 23,00,000 | Needs = 30,00,000 + 3,60,000 x 10 + 15,00,000 = 81,00,000; less 8,00,000 and 50,00,000 = Rs. 23,00,000. |
| 2 | Years to reach a target (NPER) | 9 years | FV/PV = 1.9990; n = ln(1.9990) / ln(1.08) = 9 years. |
| 3 | Net worth statement | Rs. 84,50,000 | Assets 1,17,00,000 - liabilities 32,50,000 = Rs. 84,50,000. |
| 4 | Interest and principal in the first EMI | Rs. 5,989 | Interest = 40,00,000 x 0.00750 = Rs. 30,000; principal = 35,989.04 - Rs. 30,000 = Rs. 5,989. |
| 5 | Market cap to GDP | 107.1% | 300 / 280 = 107.1%. |
| 7 | Real value of a future amount | Rs. 14,61,380 | 20,00,000 / 1.04^8 = Rs. 14,61,380. |
| 8 | Bonus issue price adjustment | Rs. 675.00 | 900 / (1 + 1/3) = Rs. 675.00. |
| 8 | Price from target P/E | Rs. 690.00 | Forward EPS = 30 x 1.15 = 34.50; x 20 = Rs. 690.00. |
| 9 | Tax-equivalent yield | 8.57% | 6 / (1 - 0.30) = 8.57%. |
| 10 | Covered call profit | Rs. 5,200 | [min(870,840) - 800 + 12] x 100 = Rs. 5,200. |
| 10 | Short put option writer P&L | Rs. -2,500 | [20 - 25] x 500 = Rs. -2,500. |
| 11 | Portfolio turnover ratio | 20.00% | min(600, 240) / 1200 = 20.00%. |
| 12 | PMS: fixed fee vs profit-sharing structure | Rs. 0.50 lakh | Plan 1 = 2.50; Plan 2 = 2.00; difference = Rs. 0.50 lakh. |
| 13 | AIF drawdown and undrawn commitment | Rs. 0.80 crore | 2 x 0.30 x 2 = 1.20; undrawn = Rs. 0.80 crore. |
| 14 | Covariance and correlation | 0.50 | rho = 0.5, cov = 0.5 x 10 x 8 = 40.00; answer 0.50. |
| 14 | Sharpe ratio | 0.39 | (14 - 7) / 18 = 0.39. |
| 15 | Rebalancing trade to target weights | Rs. 28,80,000 | Equity = Rs. 1,00,00,000; debt = Rs. 42,40,000; total = Rs. 1,42,40,000; target equity = Rs. 71,20,000; sell = Rs. 28,80,000. |
| 16 | Up- and down-capture ratio | 90.0% | Up = 4.2/3.0 = 140.0%; down = -1.8/-2.0 = 90.0%. |
| 17 | Custody fee | Rs. 40,52,500 | 8,00,00,00,000 x 5/10000 = Rs. 40,00,000; plus 350 x 150 = 52,500; total = Rs. 40,52,500. |
| 18 | Slab-wise maximum expense ratio (stated) | Rs. 15.25 crore | 500 x 2.25% + 200 x 2.0% = Rs. 15.25 crore. |
Yes. Chapters on time value of money, cash-flow and debt management, stocks, fixed income, derivatives, modern portfolio theory and performance measurement 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 has 90 MCQs plus 9 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-A 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-A mock, read the X-A notes and question bank, or start with the chapters that have the most numericals: Time Value of Money, Investing in Stocks, Investing in Fixed Income Securities.
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