CFA Level I Formulas & Calculators
Plug in your numbers and see every result worked out, step by step — then use the reference below to recognise which formula a question is really asking for.
← Back to the full “How to pass CFA Level I” guideStudy aid only, not financial advice
These calculators practice the standard exam formulas so you can check your working. They are for exam preparation only. Real financial decisions involve taxes, fees, inflation, and risk that these formulas do not model.
Future value (savings growth)
Grow a starting amount plus regular contributions at a periodic rate.
Future value
PV(1+r)^N + PMT annuity
…growth on the starting amount
PV(1+r)^N
…value of the contributions
Present value (discounting)
What a future sum (and/or recurring cash flow) is worth today.
Present value
FV ÷ (1+r)^N + PMT annuity
Effective annual rate (EAR)
The true annual rate once compounding is included.
Effective annual rate
(1 + i/m)^m − 1
Compound annual growth rate (CAGR)
The smoothed annual growth rate between two values.
CAGR
(End ÷ Begin)^(1/years) − 1
Formula reference
What each formula means and when to reach for it on exam day.
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Future value (lump sum)
FV = PV × (1 + r)^N
What a sum grows to after N periods at rate r.
When: Compounding a single cash flow forward.
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Present value (lump sum)
PV = FV ÷ (1 + r)^N
What a future sum is worth today.
When: Discounting a single future cash flow.
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Present value of an annuity
PV = PMT × [1 − (1 + r)^−N] ÷ r
Today’s value of a level stream of payments.
When: Bond coupons, loan payments, retirement income.
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Effective annual rate
EAR = (1 + i/m)^m − 1
The true annual rate once compounding is counted.
When: Comparing quoted rates with different compounding.
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Holding period return
HPR = (P₁ − P₀ + income) ÷ P₀
Total return over a single holding period.
When: Measuring realized return including income.
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Sharpe ratio
Sharpe = (Rₚ − R_f) ÷ σₚ
Excess return earned per unit of total risk.
When: Comparing risk-adjusted performance of portfolios.
Frequently asked questions
- Which calculators are allowed on the CFA exam?
- Only two models: the Texas Instruments BA II Plus (including the BA II Plus Professional) and the Hewlett-Packard 12C (including its variants). Master the time-value-of-money keys on whichever you pick before exam day.
- What quantitative formulas are on CFA Level I?
- Time value of money (future and present value, annuities), the effective annual rate, holding-period return, and risk-adjusted measures such as the Sharpe ratio recur across quantitative methods, equity, fixed income, and portfolio management.