Finance formula flashcards: TVM, duration, VaR, CAPM

0 of 11 cards done · 11 still in the round · 0 answers so far

Future value

A single amount after n periods

Say or write the formula, then show the answer.

Keys: Enter or Space shows the answer; 1 not yet, 2 partly, 3 knew it. Nothing is saved: reloading the page or changing the deck starts a new round.

Key facts

Six decks: time value of money (11 cards), bonds and duration (7), value at risk and volatility (8), CAPM and portfolio risk (7), and the whole Level I (48) and Part I (38) sheets.
Each card has a formula’s name and use on one side and the formula with a check calculation on the other; either side can be the front.
Missed cards come back after three other cards; recalled and partly recalled cards go to the back of the stack.
A card leaves the round after two correct recalls in a row (one to three, as you choose), because dropping items after a single recall loses much of the benefit of retrieval practice.
The round lives only in the open page: no account, no cookies, nothing stored.

How is the result calculated?

Each card is one row of our Level I formula sheet or Part I formula sheet: the name and use on one side, the formula and its check value on the other. You recall, show the answer and rate how well you knew it. The round then decides what comes next:

Knew it: the card goes to the back of the stack. After $k$ correct recalls in a row (two unless you change it) it leaves the round.
Partly: counts as not recalled – the streak starts again and the card goes to the back.
Not yet: the card comes back after $g = 3$ other cards, or at the back when fewer are left.

\text{position of a missed card} = \min(g,\ m) + 1, \qquad A_{\min} = N \times k

$m$ is the number of other cards still in the round and $A_{\min}$ the fewest answers a round of $N$ cards can take. The rules follow the research on retrieval practice. Testing yourself beats rereading for what you still know a week later (Roediger and Karpicke, 2006), and practice testing and spreading practice out are the two techniques a large review rated most useful (Dunlosky et al., 2013). Dropping a word pair from testing once it had been recalled cost much of that gain, while dropping it from study did not (Karpicke and Roediger, 2008) – hence the second recall. And one large stack, in which each card waits for the others, beat the same cards studied in small stacks for 90% of learners in Kornell’s experiments, although 72% believed the small stacks had worked better (Kornell, 2009) – hence the back of the stack rather than the next card.

Worked example

A short round with the first four cards of the time value of money deck (Future value, Present value, Ordinary annuity, Annuity due), each needing two correct recalls in a row:

A practice round, answer by answer
Answer	Card	Rating	What happens	Cards left
1	Future value	Knew it	Recalled: to the back of the stack	4
2	Present value	Not yet	Missed: back after three other cards	4
3	Ordinary annuity	Knew it	Recalled: to the back of the stack	4
4	Annuity due	Partly	Partly: to the back, the streak starts again	4
5	Future value	Knew it	Second recall in a row: leaves the round	3
6	Present value	Knew it	Recalled: to the back of the stack	3
7	Ordinary annuity	Knew it	Second recall in a row: leaves the round	2
8	Annuity due	Knew it	Recalled: to the back of the stack	2
9	Present value	Knew it	Second recall in a row: leaves the round	1
10	Annuity due	Knew it	Second recall in a row: leaves the round	0

The round took 10 answers – 2 more than the minimum of 8, one for the missed card and one for the partly known one. Present value, missed at answer 2, came back after three other cards, and Annuity due, only partly known at answer 4, had to be recalled twice more before it could leave.

How should you use the flashcards?

Recall before you look. Say the formula out loud or write it on paper, then press Show answer. Recognising a formula on the screen feels like knowing it; producing it is the test.
Rate honestly. Knew it means you produced the whole formula with the right signs and terms. A missing term or a wrong sign is Partly, and the card comes back.
Keep rounds short and frequent. A focus deck of 7 to 11 cards takes at least 14 to 22 answers at the default setting. Come back to it on another day rather than repeating it straight away.
Work the check value. Each answer has the inputs and result of a check calculation. Rework it on your calculator for the cards you missed – the time value of money calculator and the value at risk calculator show the working.
Turn the cards round. Once a deck goes smoothly, set the front to the formula: naming a formula and its use is what you need when it turns up in a worked solution.

Which mistakes are common?

Dropping a card after the first correct recall. That is exactly the habit the research above warns against; the second recall is where much of the benefit lies.
Cramming small piles. Five cards over and over feel productive because the answers are fresh. A bigger stack, where each card waits, is harder in the moment and better on a later test (Kornell, 2009).
Learning the formula without the conditions. The square-root-of-time rule needs independent, identically distributed returns; the Gordon growth model needs r above g. The use line on each card says when a formula applies.
Treating the cards as the syllabus. The 86 formulas are our own selection of textbook formulas under general topic names, not a list of what the exams test. Use them beside the curriculum and practice questions.

What this tool covers

Last updated

30 October 2026

Based on

The rows of our Level I and Part I formula sheets (textbook formulas with check values)
Research on retrieval practice and spacing for the order of the round
Your own ratings

Includes

Four focus decks and both sheets in full
Name-to-formula or formula-to-name practice, shuffled or in sheet order
Repeats within the round and a list of the cards that needed another go

Not included

Saved progress or scheduling across days
Exam questions or syllabus wording
Formulas that are not on the two sheets

Frequently asked questions

Which formulas are on the cards?

The 86 formulas of our Level I and Part I formula sheets. The focus decks cover time value of money (11 cards), bonds and duration (7), value at risk and volatility (8), and CAPM and portfolio risk (7).

How does the round decide which card comes next?

A recalled card goes to the back of the stack, a partly recalled one too but with its streak reset, and a missed card comes back after three other cards. A card leaves after two correct recalls in a row.

Why does a card I knew come back?

Because recalling it again is what makes it last. In Karpicke and Roediger’s experiment, dropping items from testing once they had been recalled cost much of the long-term benefit; dropping them from study did not.

Should I shuffle the cards?

Once you know a deck in sheet order, yes: shuffling stops you leaning on the order of the sheet. Turning the cards round, with the formula on the front, is the next step.

Do the cards cover everything for the exam?

No. They hold our own selection of textbook formulas under general topic names, not a list of what the exams test. Use them beside the curriculum and practice questions.

Does the tool save my progress?

No. The round lives only in the open page; reloading or changing the deck starts a new one. The address after the # sign keeps the deck and settings, so you can bookmark or share them.

Can I use the flashcards with a keyboard?

Yes. Enter or Space shows the answer, and the keys 1, 2 and 3 rate it as not yet, partly or knew it. The focus moves to the answer and then to the next card.

Sources

Roediger, H. L. & Karpicke, J. D., Psychological Science 17(3), 249–255: Test-enhanced learning: Taking memory tests improves long-term retention (2006).
Karpicke, J. D. & Roediger, H. L., Science 319(5865), 966–968: The critical importance of retrieval for learning (2008).
Kornell, N., Applied Cognitive Psychology 23(9), 1297–1317: Optimising learning using flashcards: Spacing is more effective than cramming (2009).
Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J. & Willingham, D. T., Psychological Science in the Public Interest 14(1), 4–58: Improving students’ learning with effective learning techniques (2013).
Aswath Damodaran, NYU Stern School of Business (secondary source): A Primer on the Time Value of Money. Accessed 29 October 2026.
Aswath Damodaran, NYU Stern School of Business (secondary source): A Primer on Statistics — covariance and correlation. Accessed 29 October 2026.
Yen-Chi Chen, University of Washington (lecture notes, secondary source): STAT 535, Lecture 1: Review on Probability and Statistics — expectation, covariance and total expectation. Accessed 29 October 2026.
National Institute of Standards and Technology (statistical handbook, secondary source): NIST/SEMATECH e-Handbook §1.3.5.2 — Confidence limits for the mean and the t test statistic. Accessed 30 October 2026.
National Institute of Standards and Technology (statistical handbook, secondary source): NIST/SEMATECH e-Handbook §1.3.5.11 — Measures of skewness and kurtosis. Accessed 30 October 2026.
Association of Chartered Certified Accountants (technical article, secondary source): Financial statements interpretation — profitability, liquidity, activity and gearing. Accessed 29 October 2026.
Business Development Bank of Canada (financial education, secondary source): Quick ratio calculator — eligible quick assets and current liabilities. Accessed 29 October 2026.
Corporate Finance Institute (financial education, secondary source): Cash Conversion Cycle — days inventory outstanding + days sales outstanding − days payables outstanding (11 September 2019). Accessed 30 October 2026.
Aswath Damodaran, NYU Stern School of Business (academic primer, secondary source): A Primer on Financial Statements — profitability, book equity, leverage and interest coverage. Accessed 29 October 2026.
American Association of Individual Investors (analytical article, secondary source): Deconstructing ROE: DuPont Analysis — three-step and five-step decompositions. Accessed 29 October 2026.
Texas Instruments: Solution 11241: Computing Net Present Value (NPV) and Internal Rate of Return (IRR) Using the BA II PLUS and the BA II PLUS PROFESSIONAL. Accessed 29 October 2026.
Aswath Damodaran, NYU Stern School of Business (secondary source): The Little Book of Valuation — Discount rates: cost of capital as a weighted average, after-tax cost of debt. Accessed 30 October 2026.
Aswath Damodaran, NYU Stern School of Business (lecture notes, secondary source): Discounted cashflow models — I. The stable growth DDM: Gordon growth model; stable-period payout ratio 1 − g/ROE. Accessed 30 October 2026.
International Monetary Fund (methods overview, secondary source): A Primer on Managing Sovereign Debt-Portfolio Risks — Macaulay and modified duration (Working Paper 2018/074). Accessed 29 October 2026.
Reserve Bank of India (educational primer, secondary source): Government Securities Market in India — A Primer: full price; §27, duration, PV01 and convexity. Accessed 29 October 2026.
CME Group (market education, secondary source): How Can You Measure Risk in Treasuries? — Value of a basis point and modified duration. Accessed 29 October 2026.
International Monetary Fund: Financial Soundness Indicators: Compilation Guide — Appendix VI, §§50–55: convexity and the term structure. Accessed 29 October 2026.
Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Forward and Futures Prices — no-arbitrage replication, income, contract value and settlement timing. Accessed 29 October 2026.
Kerry Back, Hong Liu and Mark Loewenstein (academic textbook, secondary source): Pricing and Hedging Derivative Securities — Chapter 3, §§3.2–3.3: expectations, cost of carry and convenience yield. Accessed 29 October 2026.
Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Properties of European Options — put-call parity and matching terminal payoffs. Accessed 29 October 2026.
Kerry Back, Hong Liu and Mark Loewenstein (academic textbook, secondary source): Pricing and Hedging Derivative Securities — Chapter 4, §§4.1–4.4 and Exercise 4.8: replication, risk-neutral pricing, backward induction, tree calibration and convergence. Accessed 29 October 2026.
Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): Portfolios of Risky Assets — expected return, covariance, portfolio variance and the minimum-variance frontier. Accessed 29 October 2026.
Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): The Capital Asset Pricing Model — assumptions, beta, systematic risk and model limitations. Accessed 29 October 2026.
William F. Sharpe, Stanford University (academic notes, secondary source): Macro-Investment Analysis: Equilibrium (preliminary) — Expected Return and Beta Values; The Market Portfolio and the Security Market Line. Accessed 29 October 2026.
William F. Sharpe, The Journal of Portfolio Management (author's Stanford reprint): The Sharpe Ratio — The Ratio, Time Dependence, Correlations and Related Measures (1994). Accessed 29 October 2026.
Kevin Sheppard, arch (Python package) documentation (secondary source): arch.univariate.EWMAVariance — exponentially weighted moving-average (RiskMetrics) variance, default λ = 0.94. Accessed 30 October 2026.
NYU Stern Volatility and Risk Institute (model documentation, secondary source): V-Lab: GARCH volatility documentation — the GARCH(1,1) recursion and long-run variance ω/(1 − α − β). Accessed 30 October 2026.
Wolfram Formula Repository (secondary source): Minimum Variance Hedge Ratio — h* = ρσ_S/σ_F for spot and futures price changes. Accessed 30 October 2026.
Wolfram Formula Repository (secondary source): Commodity Contracts Optimal Number — N* = h* × position size ÷ futures contract value. Accessed 30 October 2026.
Lorenzo Naranjo, Washington University in St. Louis (lecture notes, secondary source): The Impact of Dividends — put-call parity adjusted for the present value of cash dividends. Accessed 29 October 2026.
Colleen Cassidy and Marianne Gizycki, Reserve Bank of Australia (methods overview, secondary source): Measuring Traded Market Risk: Value-at-risk and Backtesting Techniques — 2. Value-at-risk (November 1997). Accessed 29 October 2026.
Michael Papaioannou, International Monetary Fund (secondary source): A Primer for Risk Measurement of Bonded Debt from the Perspective of a Sovereign Debt Manager — Appendix II (Working Paper 2006/195) (August 2006). Accessed 29 October 2026.
Carlo Acerbi and Dirk Tasche, arXiv: On the coherence of Expected Shortfall — arXiv v5; definitions 2.1, 2.2 and 2.6; proposition 3.2 (2 May 2002). Accessed 29 October 2026.
Kerry Back, Hong Liu and Mark Loewenstein (academic textbook, secondary source): Pricing and Hedging Derivative Securities — Chapter 9: Greeks, discrete delta hedging and delta-gamma hedging. Accessed 29 October 2026.
Basel Committee on Banking Supervision, Bank for International Settlements: Basel Framework CRE35.1–35.9 — IRB expected losses, eligible provisions and capital treatment. Accessed 29 October 2026.
National Institute of Standards and Technology (statistical handbook, secondary source): NIST/SEMATECH e-Handbook §1.3.6.6.18 — Binomial distribution: mean and standard deviation. Accessed 29 October 2026.

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