CFP Exam Formula Cheat Sheet
Every essential formula organized by topic. Bookmark this page and review daily.
⏰Time Value of Money (TVM)
| Formula Name | Formula | Notes |
|---|---|---|
| Future Value (Single Sum) | FV = PV × (1 + r)ⁿ | PV = present value, r = rate per period, n = number of periods |
| Present Value (Single Sum) | PV = FV ÷ (1 + r)ⁿ | Discounting a future cash flow back to today |
| Future Value of Annuity | FVA = PMT × [((1 + r)ⁿ - 1) ÷ r] | For ordinary annuity (payments at end of period) |
| Present Value of Annuity | PVA = PMT × [(1 - (1 + r)⁻ⁿ) ÷ r] | Discounting a stream of equal payments |
| Annuity Due Adjustment | FVA_due = FVA_ordinary × (1 + r) | Multiply ordinary annuity result by (1 + r) for beginning-of-period payments |
| Rule of 72 | Years to double ≈ 72 ÷ r | Quick estimate; r is the annual interest rate as a whole number |
| Real Rate of Return | r_real ≈ r_nominal - inflation | Approximate; exact: (1 + r_nom) ÷ (1 + inflation) - 1 |
| Effective Annual Rate (EAR) | EAR = (1 + r/n)ⁿ - 1 | r = nominal rate, n = compounding periods per year |
📈Investment Planning
| Formula Name | Formula | Notes |
|---|---|---|
| Holding Period Return | HPR = (Ending Value - Beginning Value + Income) ÷ Beginning Value | Total return over the holding period |
| Arithmetic Mean Return | R̄ = (R₁ + R₂ + ... + Rₙ) ÷ n | Simple average of returns |
| Geometric Mean Return | G = [(1+R₁)(1+R₂)...(1+Rₙ)]^(1/n) - 1 | Compound average annual return |
| Standard Deviation | σ = √[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 Ratio | S = (Rp - Rf) ÷ σp | Excess return per unit of total risk |
| Treynor Ratio | T = (Rp - Rf) ÷ βp | Excess return per unit of systematic risk |
| Jensen's Alpha | α = Rp - [Rf + βp × (Rₘ - Rf)] | Excess return above CAPM expectation |
| Information Ratio | IR = (Rp - Rb) ÷ Tracking Error | Active return per unit of active risk |
| Current Yield (Bond) | CY = Annual Coupon ÷ Current Market Price | Does not account for capital gains/losses |
| Dividend Discount Model | P₀ = D₁ ÷ (r - g) | Gordon Growth Model; r = required return, g = constant growth rate |
| P/E Ratio | P/E = Price per Share ÷ EPS | Earnings per share valuation metric |
| Portfolio Return | Rp = Σ(wᵢ × Rᵢ) | Weighted average of individual returns |
| Bond Duration | D = Σ[t × PV(CFₜ)] ÷ Price | Weighted average time to receive cash flows |
| Modified Duration | D_mod = Macaulay Duration ÷ (1 + YTM/n) | Measures price sensitivity to yield changes |
| Correlation Coefficient | ρ = Cov(A,B) ÷ (σA × σB) | Ranges from -1 to +1; key for diversification |
🏖️Retirement Planning
| Formula Name | Formula | Notes |
|---|---|---|
| Replacement Ratio | RR = Retirement Income Need ÷ Pre-Retirement Income | Typically 70-80% of pre-retirement income |
| Capital Needs Analysis | PV of Retirement Needs = Annual Need × PVA factor | Calculate total savings needed at retirement |
| Wage Replacement Ratio | WRR = (Pre-retirement expenses - savings - FICA) ÷ Gross income | More precise than general 70-80% estimate |
| Social Security Benefit | PIA = f(AIME, bend points) | Based on 35 highest-earning years, adjusted for inflation |
| Required Minimum Distribution | RMD = Account Balance ÷ Distribution Period | From Uniform Lifetime Table; begins at age 73 (SECURE 2.0) |
| Annual Savings Needed | PMT = FV_need ÷ FVA factor | Solve for PMT given retirement goal and years to save |
| Inflation-Adjusted Withdrawal | Withdrawal = Previous Year × (1 + inflation) | Maintains purchasing power in retirement |
| 4% Rule | First Year Withdrawal = Portfolio × 0.04 | Then adjust for inflation annually (Trinity Study) |
📋Tax Planning
| Formula Name | Formula | Notes |
|---|---|---|
| Marginal Tax Rate | MTR = ΔTax ÷ ΔIncome | Tax rate on the next dollar of income |
| Effective Tax Rate | ETR = Total Tax ÷ Gross Income | Average rate across all income |
| After-Tax Return | r_at = r × (1 - t) | For interest income; t = marginal tax rate |
| Tax-Equivalent Yield | TEY = Muni Yield ÷ (1 - t) | Compare tax-exempt to taxable bonds |
| Taxable Equivalent | Taxable Yield = Tax-Exempt Yield ÷ (1 - Marginal Rate) | What a taxable bond must yield to match muni |
| Capital Gains Tax | CGT = (Sale Price - Basis) × CG Rate | LTCG rates: 0%, 15%, or 20% + 3.8% NIIT if applicable |
| AMT | AMT = (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 Name | Formula | Notes |
|---|---|---|
| Human Life Value | HLV = PV of future earnings - self-maintenance | Estimates total economic value of a person's earning potential |
| Needs Approach | Insurance Need = PV(Obligations) - Existing Resources | Cash needs, income replacement, special needs minus assets |
| Net Single Premium | NSP = PV of Expected Claims | Pure cost of insurance before loading |
| Disability Insurance Need | Need = Annual Income × % to Replace × Years Until Retirement | Typically replace 60-70% of gross income |
| Long-Term Care Daily Benefit | Benefit = Local Daily Rate × Inflation Factor | Project forward to likely need date |
| Coinsurance Penalty | Payout = (Coverage ÷ Required) × Loss - Deductible | Applies when insured carries less than required % |
⚖️Estate Planning
| Formula Name | Formula | Notes |
|---|---|---|
| Gross Estate | GE = All assets + Insurance + Annuities + Joint property + Transfers | Everything included in estate at death |
| Taxable Estate | TE = Gross Estate - Deductions - Marital Deduction - Charitable | Amount subject to estate tax |
| Unified Credit | $13.61M (2024) per person | Applicable exclusion amount; portability available between spouses |
| Estate Tax Due | Tax = (Taxable Estate × 40%) - Unified Credit | Top marginal rate is 40% for amounts over exclusion |
| Generation-Skipping Transfer Tax | GSTT = Transfer Amount × 40% | Separate $13.61M exemption (2024) |
| Charitable Remainder Trust | Deduction = FMV of Property - PV of Income Interest | Annuity trust (CRAT) or unitrust (CRUT) |
| Annual Gift Exclusion Strategy | Total Excluded = $18,000 × Donees × Years × Donors | Married couple giving to 3 people = $108K/year estate reduction |
| Irrevocable Life Insurance Trust | Death Benefit excluded from estate | Must survive 3-year lookback; Crummey notices required |
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