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” guideFuture 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.