CFPDatabase

CFP Exam Formula Cheat Sheet

Every essential formula organized by topic. Bookmark this page and review daily.

Time Value of Money (TVM)

Formula NameFormulaNotes
Future Value (Single Sum)FV = PV × (1 + r)ⁿPV = present value, r = rate per period, n = number of periods
Present Value (Single Sum)PV = FV ÷ (1 + r)ⁿDiscounting a future cash flow back to today
Future Value of AnnuityFVA = PMT × [((1 + r)ⁿ - 1) ÷ r]For ordinary annuity (payments at end of period)
Present Value of AnnuityPVA = PMT × [(1 - (1 + r)⁻ⁿ) ÷ r]Discounting a stream of equal payments
Annuity Due AdjustmentFVA_due = FVA_ordinary × (1 + r)Multiply ordinary annuity result by (1 + r) for beginning-of-period payments
Rule of 72Years to double ≈ 72 ÷ rQuick estimate; r is the annual interest rate as a whole number
Real Rate of Returnr_real ≈ r_nominal - inflationApproximate; exact: (1 + r_nom) ÷ (1 + inflation) - 1
Effective Annual Rate (EAR)EAR = (1 + r/n)ⁿ - 1r = nominal rate, n = compounding periods per year

📈Investment Planning

Formula NameFormulaNotes
Holding Period ReturnHPR = (Ending Value - Beginning Value + Income) ÷ Beginning ValueTotal return over the holding period
Arithmetic Mean ReturnR̄ = (R₁ + R₂ + ... + Rₙ) ÷ nSimple average of returns
Geometric Mean ReturnG = [(1+R₁)(1+R₂)...(1+Rₙ)]^(1/n) - 1Compound average annual return
Standard Deviationσ = √[Σ(Rᵢ - R̄)² ÷ (n - 1)]Measures total risk (volatility)
Beta (β)β = Cov(Rᵢ, Rₘ) ÷ Var(Rₘ)Systematic risk relative to market
CAPM (Required Return)E(Rᵢ) = Rf + βᵢ × (Rₘ - Rf)Rf = risk-free rate, Rₘ = market return
Sharpe RatioS = (Rp - Rf) ÷ σpExcess return per unit of total risk
Treynor RatioT = (Rp - Rf) ÷ βpExcess return per unit of systematic risk
Jensen's Alphaα = Rp - [Rf + βp × (Rₘ - Rf)]Excess return above CAPM expectation
Information RatioIR = (Rp - Rb) ÷ Tracking ErrorActive return per unit of active risk
Current Yield (Bond)CY = Annual Coupon ÷ Current Market PriceDoes not account for capital gains/losses
Dividend Discount ModelP₀ = D₁ ÷ (r - g)Gordon Growth Model; r = required return, g = constant growth rate
P/E RatioP/E = Price per Share ÷ EPSEarnings per share valuation metric
Portfolio ReturnRp = Σ(wᵢ × Rᵢ)Weighted average of individual returns
Bond DurationD = Σ[t × PV(CFₜ)] ÷ PriceWeighted average time to receive cash flows
Modified DurationD_mod = Macaulay Duration ÷ (1 + YTM/n)Measures price sensitivity to yield changes
Correlation Coefficientρ = Cov(A,B) ÷ (σA × σB)Ranges from -1 to +1; key for diversification

🏖️Retirement Planning

Formula NameFormulaNotes
Replacement RatioRR = Retirement Income Need ÷ Pre-Retirement IncomeTypically 70-80% of pre-retirement income
Capital Needs AnalysisPV of Retirement Needs = Annual Need × PVA factorCalculate total savings needed at retirement
Wage Replacement RatioWRR = (Pre-retirement expenses - savings - FICA) ÷ Gross incomeMore precise than general 70-80% estimate
Social Security BenefitPIA = f(AIME, bend points)Based on 35 highest-earning years, adjusted for inflation
Required Minimum DistributionRMD = Account Balance ÷ Distribution PeriodFrom Uniform Lifetime Table; begins at age 73 (SECURE 2.0)
Annual Savings NeededPMT = FV_need ÷ FVA factorSolve for PMT given retirement goal and years to save
Inflation-Adjusted WithdrawalWithdrawal = Previous Year × (1 + inflation)Maintains purchasing power in retirement
4% RuleFirst Year Withdrawal = Portfolio × 0.04Then adjust for inflation annually (Trinity Study)

📋Tax Planning

Formula NameFormulaNotes
Marginal Tax RateMTR = ΔTax ÷ ΔIncomeTax rate on the next dollar of income
Effective Tax RateETR = Total Tax ÷ Gross IncomeAverage rate across all income
After-Tax Returnr_at = r × (1 - t)For interest income; t = marginal tax rate
Tax-Equivalent YieldTEY = Muni Yield ÷ (1 - t)Compare tax-exempt to taxable bonds
Taxable EquivalentTaxable Yield = Tax-Exempt Yield ÷ (1 - Marginal Rate)What a taxable bond must yield to match muni
Capital Gains TaxCGT = (Sale Price - Basis) × CG RateLTCG rates: 0%, 15%, or 20% + 3.8% NIIT if applicable
AMTAMT = (AMTI - Exemption) × 26% or 28%Alternative Minimum Tax calculation
Gift Tax Annual Exclusion$18,000 per donee (2024)Married couples: $36,000 per donee via split gifts

🛡️Insurance & Risk Management

Formula NameFormulaNotes
Human Life ValueHLV = PV of future earnings - self-maintenanceEstimates total economic value of a person's earning potential
Needs ApproachInsurance Need = PV(Obligations) - Existing ResourcesCash needs, income replacement, special needs minus assets
Net Single PremiumNSP = PV of Expected ClaimsPure cost of insurance before loading
Disability Insurance NeedNeed = Annual Income × % to Replace × Years Until RetirementTypically replace 60-70% of gross income
Long-Term Care Daily BenefitBenefit = Local Daily Rate × Inflation FactorProject forward to likely need date
Coinsurance PenaltyPayout = (Coverage ÷ Required) × Loss - DeductibleApplies when insured carries less than required %

⚖️Estate Planning

Formula NameFormulaNotes
Gross EstateGE = All assets + Insurance + Annuities + Joint property + TransfersEverything included in estate at death
Taxable EstateTE = Gross Estate - Deductions - Marital Deduction - CharitableAmount subject to estate tax
Unified Credit$13.61M (2024) per personApplicable exclusion amount; portability available between spouses
Estate Tax DueTax = (Taxable Estate × 40%) - Unified CreditTop marginal rate is 40% for amounts over exclusion
Generation-Skipping Transfer TaxGSTT = Transfer Amount × 40%Separate $13.61M exemption (2024)
Charitable Remainder TrustDeduction = FMV of Property - PV of Income InterestAnnuity trust (CRAT) or unitrust (CRUT)
Annual Gift Exclusion StrategyTotal Excluded = $18,000 × Donees × Years × DonorsMarried couple giving to 3 people = $108K/year estate reduction
Irrevocable Life Insurance TrustDeath Benefit excluded from estateMust survive 3-year lookback; Crummey notices required

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