Most Important CFA Quantitative Methods Formulas

Quantitative Methods underpins most of the rest of the CFA Level 1 curriculum — the discounting logic you learn here reappears in Fixed Income and Equity valuation, and the statistical concepts reappear in Portfolio Management. Below are the formulas that show up most often, grouped by the area of Quant they belong to. Knowing a formula is necessary but not sufficient — the exam tests whether you can recognize which formula a scenario calls for, which is exactly what scenario-based practice questions are for.

Time value of money

Future value of a single sum: FV = PV × (1 + r)^n

Present value of a single sum: PV = FV ÷ (1 + r)^n

Future value of an ordinary annuity: FV = PMT × [(1 + r)^n − 1] ÷ r

Present value of an ordinary annuity: PV = PMT × [1 − (1 + r)^−n] ÷ r

For an annuity due (payments at the start of each period rather than the end), multiply the ordinary annuity result by (1 + r).

Effective annual rate (EAR), given a stated annual rate compounded m times per year: EAR = (1 + r_stated ÷ m)^m − 1

Watch for questions that give you a stated (nominal) rate with a compounding frequency and ask for the effective rate, or vice versa — mixing these up is one of the most common Quant errors.

Discounted cash flow applications

Net present value: NPV = Σ [CF_t ÷ (1 + r)^t] − Initial outlay

Internal rate of return (IRR): the discount rate that makes NPV equal to zero. You won’t solve for IRR by hand on most Level 1 questions — you’re tested on interpreting it (accept a project if IRR exceeds the required rate of return) rather than computing it algebraically.

Holding period return: HPR = (Ending value − Beginning value + Income) ÷ Beginning value

Probability

Expected value of a random variable: E(X) = Σ [P(X_i) × X_i]

Variance of a random variable: Var(X) = Σ [P(X_i) × (X_i − E(X))²]

Covariance between two random variables: Cov(X,Y) = Σ [P(X_i, Y_i) × (X_i − E(X)) × (Y_i − E(Y))]

Correlation coefficient: ρ(X,Y) = Cov(X,Y) ÷ [σ(X) × σ(Y)]

Correlation is bounded between −1 and 1 by construction; if a calculated value falls outside that range, there’s an arithmetic error. This is a useful sanity check under exam time pressure.

Bayes’ formula (updating a probability given new information): P(A|B) = [P(B|A) × P(A)] ÷ P(B)

Sampling and estimation

Standard error of the sample mean: SE = σ ÷ √n (population standard deviation known) SE = s ÷ √n (sample standard deviation used as an estimate)

Confidence interval for a population mean: CI = x̄ ± (critical value × standard error)

Which critical value to use — z or t — depends on whether the population variance is known and on sample size. Small samples from a population with unknown variance require the t-distribution; large samples are commonly approximated using z.

Hypothesis testing

Test statistic for a sample mean (z-test, population variance known): z = (x̄ − μ₀) ÷ (σ ÷ √n)

Test statistic for a sample mean (t-test, population variance unknown): t = (x̄ − μ₀) ÷ (s ÷ √n)

The exam tests the logic of hypothesis testing at least as much as the calculation: stating the null and alternative hypotheses correctly, choosing the right test statistic, and interpreting a result relative to a significance level. A common wrong answer flips the conclusion — failing to reject a null hypothesis is not the same as proving it true.

Regression (introductory)

Simple linear regression equation: Y = b₀ + b₁X + ε

Slope coefficient: b₁ = Cov(X,Y) ÷ Var(X)

At Level 1, you’re mainly tested on interpreting regression output — the meaning of the slope coefficient, the R², and statistical significance of the coefficients — rather than deriving them from raw data.

How to actually retain these

Formulas memorized in isolation fade quickly under exam pressure. The more durable approach is to work through scenario-based Quantitative Methods practice questions where each formula is applied to a specific situation — a bond’s future value, an investment’s expected return, a hypothesis about a portfolio’s average return — so you’re building recognition of when to reach for a formula, not just what it says. Pair this with the 90-day CFA Level 1 study plan to sequence Quant review alongside the topics that depend on it.