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Finance · Formula sheet

Finance formulas

One printable sheet for 32 Finance tools — formulas collected from each calculator’s How it works.

Finance calculators →

APY Calculator

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\[ \mathrm{APY} = \left(1+\frac{r}{m}\right)^{m} - 1 \]

Raise one plus the period rate to the number of compounds, then subtract one.

Cash Flow to Debt Ratio Calculator

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\[ \text{Ratio} = \frac{\text{Cash flow}}{\text{Total debt}} \]

Divide cash flow from operations by total debt.

Cash Ratio Calculator

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\[ \text{Cash ratio} = \frac{\text{Cash} + \text{Equivalents}}{\text{Current liabilities}} \]

Add cash and equivalents, then divide by current liabilities.

Certificate of Deposit Calculator

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\[ FV = P\left(1+\frac{r}{m}\right)^{mt} \]

Compound the principal at the annual rate, divided across compounding periods.

Compound Annual Growth Rate (CAGR) Calculator

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\[ \mathrm{CAGR} = \left(\frac{V_{\text{end}}}{V_{\text{start}}}\right)^{1/t} - 1 \]

Raise the end/start ratio to 1/years, then subtract one.

Compound Interest Rate Calculator

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\[ r = m\left(\left(\frac{FV}{P}\right)^{1/(mt)} - 1\right) \]

Rearrange FV = P(1 + r/m)^(mt) for r.

Current Ratio Calculator

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\[ \text{Current ratio} = \frac{\text{Current assets}}{\text{Current liabilities}} \]

Divide current assets by current liabilities.

DCA Investment Calculator

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\[ FV=\mathrm{PMT}\frac{(1+i)^{N}-1}{i} \]

Enter Deposit each period ($), Annual rate (%), Years, and Periods per year for the DCA Investment Calculator; enter percentage fields as percentage points and retain the units printed in each label. The calculator reports Future value, Contributed, and Growth: Dollar-cost averaging with equal deposits each period. Future value assumes equal end-of-period deposits and a constant return.

Debt Payoff Calculator

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\[ n=\frac{\ln(p/(p-Br))}{\ln(1+r)} \]

Enter Balance ($), APR (%), and Monthly payment ($) for the Debt Payoff Calculator; enter percentage fields as percentage points and retain the units printed in each label. The calculator reports Months and Total interest: Amortizing payoff time for one debt balance. Monthly payment must exceed accrued monthly interest or the balance will not amortize.

Dividend Calculator

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\[ \text{Yield} = \frac{\text{DPS}}{\text{Price}} \times 100 \]

Annual income is shares times dividend per share. Yield compares DPS to price.

Dividend Discount Model Calculator

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\[ P = \frac{D_{1}}{r - g} \]

Divide next expected dividend by the difference between required return and growth.

Dividend Payout Ratio Calculator

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\[ \text{Payout} = \frac{\text{Dividends}}{\text{Net income}} \times 100 \]

Divide total dividends by net income and scale to percent.

Earnings per Share (EPS) Calculator

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\[ \text{EPS} = \frac{\text{Net income} - \text{Preferred dividends}}{\text{Shares}} \]

Subtract preferred dividends from net income, then divide by shares outstanding.

EBITDA Calculator

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\[ \text{EBITDA} = \text{OI} + D + A \]

Add depreciation and amortization to operating income.

Effective Interest Rate Calculator

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\[ r_{\text{eff}} = \left(1+\frac{r}{m}\right)^{m} - 1 \]

Same transform as APY from nominal rate and m compounds.

Equivalent Annual Rate (EAR) Calculator

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\[ \mathrm{EAR} = \left(1+\frac{r}{m}\right)^{m} - 1 \]

Compound the period rate over one year.

Expense Ratio Calculator

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\[ \mathrm{ER} = \frac{\text{Expenses}}{\text{Assets}} \times 100 \]

Divide fund expenses by fund assets, then convert to percent.

Expense Ratio Calculator (Cost of ETF)

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\[ C = I \times \frac{\mathrm{ER}}{100} \times t \]

Annual cost is investment times expense ratio; multi-year cost multiplies by years (simple estimate).

Forward Rate Calculator

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\[ f = \left(\frac{(1+r_{2})^{t_{2}}}{(1+r_{1})^{t_{1}}}\right)^{\frac{1}{t_{2}-t_{1}}} - 1 \]

Use the ratio of compounded spot factors between t₁ and t₂.

Future Value Calculator

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\[ FV = PV\,(1 + r)^{n} \]

Multiply present value by (1 + rate) raised to the number of periods.

Inflation Calculator

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\[ FV = PV\,(1 + i)^{t} \]

Future amount grows with inflation; purchasing power is the inverse factor.

Investment Calculator

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\[ FV = P(1+i)^{N} + \mathrm{PMT}\frac{(1+i)^{N}-1}{i} \]

Compound the principal, then add the future value of an annuity of deposits.

Loan Comparison Calculator

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\[ p=P\frac{i(1+i)^{N}}{(1+i)^{N}-1} \]

Enter Loan 1 principal, Loan 1 rate %, Loan 1 years, Loan 2 principal, Loan 2 rate %, and Loan 2 years for the Loan Comparison Calculator; enter percentage fields as percentage points and retain the units printed in each label. The calculator reports Payment 1, Payment 2, Total 1, Total 2, and Total difference: Side-by-side amortizing payment totals. The comparison excludes lender fees, insurance, and rate changes unless reflected in the inputs.

Net Profit Margin Calculator

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\[ \mathrm{NPM} = \frac{\text{Net profit}}{\text{Revenue}} \times 100 \]

Divide net profit by revenue and scale to percent.

Refinance Break-Even Calculator

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\[ t=\frac{\text{closing}}{\text{old}-\text{new}} \]

Enter Closing costs ($), Old payment ($), and New payment ($) for the Refinance Break-Even Calculator; retain the units printed in each label. The calculator reports Months to break even: Break-even months = closing costs ÷ monthly savings. Old payment must exceed New payment for a finite positive break-even time.

Return on Ad Spend (ROAS) Calculator

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\[ \text{ROAS} = \frac{\text{Revenue}}{\text{Ad spend}} \]

Divide attributed revenue by ad spend.

Return on Investment (ROI) Calculator

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\[ \text{ROI} = \frac{\text{Final} - \text{Cost}}{\text{Cost}} \times 100 \]

Subtract cost from final value, divide by cost, then scale to percent.

Rule of 72 Calculator

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\[ t\approx\frac{72}{r} \]

Enter Annual rate (%) for the Rule of 72 Calculator; enter percentage fields as percentage points. The calculator reports Years to double: Rule of 72 estimates doubling time as 72 ÷ rate%. The shortcut is most accurate for moderate positive rates with annual compounding.

Salary Calculator

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\[ \text{Hourly} = \frac{\text{Annual}}{\text{hours/week} \times 52} \]

Divide annual pay by 12, 26, or 52; hourly uses hours × 52.

Salary to Hourly Calculator

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\[ \text{Hourly} = \frac{\text{Annual}}{h \times 52} \]

Divide annual salary by hours per week times 52.

Sales Tax Calculator

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\[ \text{Tax} = P \times \frac{r}{100} \]

Tax equals price times rate; total adds tax to price.

Savings Goal Calculator

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\[ \mathrm{PMT}=\frac{(G-P(1+i)^{N})i}{(1+i)^{N}-1} \]

Enter Goal ($), Already saved ($), Annual rate (%), and Years for the Savings Goal Calculator; enter percentage fields as percentage points and retain the units printed in each label. The calculator reports Monthly deposit: Solve payment for a future-value goal with compounding. The required deposit changes if returns, timing, taxes, or fees differ from the assumptions.

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