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Finance & Interest

Interest, loans, investments and valuation

Simple Interest

Basic
I=PrtI = P r t

Interest earned on principal at a simple rate.

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Compound Interest

Basic
A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}

Value of principal compounded n times per year.

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Continuous Compounding

Advanced
A=PertA = P e^{rt}

Value with interest compounded continuously.

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Future Value

Basic
FV=PV(1+r)nFV = PV(1 + r)^n

Future worth of a present sum.

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Present Value

Basic
PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}

Present worth of a future sum.

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Future Value of Annuity

Advanced
FV=P(1+r)n1rFV = P\frac{(1+r)^n - 1}{r}

Future value of regular equal payments.

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Present Value of Annuity

Advanced
PV=P1(1+r)nrPV = P\frac{1 - (1+r)^{-n}}{r}

Present value of a series of equal payments.

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Loan EMI

Advanced
EMI=Pr(1+r)n(1+r)n1EMI = \frac{P r (1+r)^n}{(1+r)^n - 1}

Equated monthly installment on a loan.

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CAGR

Advanced
CAGR=(VfVi)1/n1CAGR = \left(\frac{V_f}{V_i}\right)^{1/n} - 1

Compound annual growth rate of an investment.

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Return on Investment

Basic
ROI=VfViVi×100%ROI = \frac{V_f - V_i}{V_i} \times 100\%

Percentage gain or loss on an investment.

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Rule of 72

Basic
t72rt \approx \frac{72}{r}

Approximate years to double an investment.

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Net Present Value

Advanced
NPV=t=0nCt(1+r)tNPV = \sum_{t=0}^{n}\frac{C_t}{(1+r)^t}

Present value of a stream of cash flows.

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Perpetuity

Advanced
PV=CrPV = \frac{C}{r}

Present value of an infinite constant cash flow.

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Straight-Line Depreciation

Basic
D=CSnD = \frac{C - S}{n}

Annual depreciation of an asset.

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Effective Annual Rate

Advanced
EAR=(1+rn)n1EAR = \left(1 + \frac{r}{n}\right)^n - 1

True annual rate accounting for compounding.

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Break-Even Point

Intermediate
Q=FCPVCQ = \frac{FC}{P - VC}

Units to sell to cover all costs.

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Profit

Basic
Profit=RevenueCost\text{Profit} = \text{Revenue} - \text{Cost}

The money left after subtracting cost from revenue.

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Profit Margin

Basic
Margin=ProfitRevenue×100%\text{Margin} = \frac{\text{Profit}}{\text{Revenue}} \times 100\%

Profit as a percentage of revenue.

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Markup

Basic
Markup=PriceCostCost×100%\text{Markup} = \frac{\text{Price} - \text{Cost}}{\text{Cost}} \times 100\%

Increase over cost as a percentage.

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Price-to-Earnings Ratio

Intermediate
PE=PriceEPSPE = \frac{\text{Price}}{\text{EPS}}

Share price relative to earnings per share.

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Earnings Per Share

Basic
EPS=Net IncomeSharesEPS = \frac{\text{Net Income}}{\text{Shares}}

Company profit allocated to each share.

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Dividend Yield

Basic
Y=DividendPrice×100Y = \frac{\text{Dividend}}{\text{Price}}\times 100

Annual dividend as a percentage of share price.

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Break-Even Point

Intermediate
Q=FCPVCQ = \frac{FC}{P - VC}

Units to sell to cover all costs.

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Gross Margin

Basic
GM=RevenueCOGSRevenue×100GM = \frac{Revenue - COGS}{Revenue}\times 100

Percentage of revenue left after cost of goods.

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Current Ratio

Intermediate
CR=Current AssetsCurrent LiabilitiesCR = \frac{\text{Current Assets}}{\text{Current Liabilities}}

Liquidity measure of short-term solvency.

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Debt-to-Equity Ratio

Intermediate
D/E=Total DebtEquityD/E = \frac{\text{Total Debt}}{\text{Equity}}

Leverage measure comparing debt to equity.

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Return on Equity

Intermediate
ROE=Net IncomeEquity×100ROE = \frac{\text{Net Income}}{\text{Equity}}\times 100

Profit generated per dollar of equity.

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Return on Assets

Intermediate
ROA=Net IncomeTotal Assets×100ROA = \frac{\text{Net Income}}{\text{Total Assets}}\times 100

Profit generated per dollar of assets.

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Real Rate of Return

Advanced
r=1+n1+i1r = \frac{1+n}{1+i} - 1

Return adjusted for inflation.

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Payback Period

Basic
PP=Initial InvestmentAnnual Cash FlowPP = \frac{\text{Initial Investment}}{\text{Annual Cash Flow}}

Time to recover an investment.

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Working Capital

Basic
WC=Current AssetsCurrent LiabilitiesWC = \text{Current Assets} - \text{Current Liabilities}

Short-term financial health of a business.

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