Mathematical & Financial Formula Hub

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Break-Even Point Formula

$$\text{Break-Even Units} = \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}$$

The break-even point calculates the exact sales volume in units or revenue required to cover total operational expenses, yielding zero net profit and zero net loss.

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Break-Even Selling Price Formula

$$\text{Break-Even Price} = \frac{\text{Total Fixed Costs} + \text{Total Variable Costs}}{\text{Expected Number of Units}}$$

The break-even selling price formula calculates the minimum price per unit required to cover all production costs for a target sales volume.

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CAGR Formula

$$CAGR = \left(\frac{EV}{BV}\right)^{\frac{1}{n}} - 1$$

Compound Annual Growth Rate (CAGR) is the geometric progression ratio that provides a constant rate of return over a specified time period. It is one of the best tools for comparing investment returns across different assets (like mutual funds vs gold vs FDs) over multi-year horizons because it smooths out volatility.

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Capital Gains Tax Calculation Formula

$$\text{Net Capital Gain} = \text{Sale Consideration} - (\text{Indexed Cost of Acquisition} + \text{Transfer Expenses})$$

Capital Gains Tax is levied on net profit realized from selling capital assets like shares, equity funds, debt funds, gold, or real estate. Holding period determines classification into Short-Term (STCG) or Long-Term (LTCG) gains.

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Compound Interest Formula

$$A = P \times \left(1 + \frac{r}{n}\right)^{nt}$$

Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods. Unlike simple interest, compound interest allows your money to grow exponentially because you earn interest on interest.

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Compound Savings Formula

$$A = P \times \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$

The Compound Savings Formula computes the total future wealth accumulated from an initial starting deposit (P) plus regular periodic additions (PMT) earning compound interest over time (t).

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Consumer Price Index (CPI) Formula

$$\text{CPI} = \left( \frac{\text{Cost of Market Basket in Current Year}}{\text{Cost of Market Basket in Base Year}} \right) \times 100$$

The Consumer Price Index (CPI) measures the average change over time in prices paid by urban consumers for a market basket of consumer goods and services.

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Credit Card Payoff Formula

$$N = -\frac{\ln\left(1 - \frac{i \cdot B}{P}\right)}{\ln(1 + i)}$$

The Credit Card Payoff Formula determines the exact number of months (N) required to liquidate a revolving credit card balance (B) at an annual interest rate (i) with a fixed monthly payment (P). Because interest compounds monthly on unpaid balances, making only minimum payments significantly extends the payoff timeline and inflates total interest costs. Paying even a small amount above the minimum drastically reduces N and cuts total interest paid.

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Debt Payoff & Snowball/Avalanche Formula

$$B_{t} = (B_{t-1} + B_{t-1} \cdot i) - (P_{\text{min}} + P_{\text{extra}} + P_{\text{rollover}})$$

The Debt Payoff Formula models the multi-debt elimination process using an amortization cascade. In every month t, interest accrues on outstanding loan balances. Mandatory minimum payments are made across all debts, while all extra funds and rolled-over payments from paid-off debts are funneled toward a single priority target debt. The priority order is determined by either the Debt Avalanche (highest APR first) or Debt Snowball (smallest balance first) method.

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Delivery Partner Earnings Formula (Swiggy, Zomato, Blinkit, Zepto)

$$\text{Gross Earnings} = \sum (\text{Base Pay} + \text{Distance Pay} + \text{Surge/Rain Pay} + \text{Waiting Pay}) + \text{Milestone Incentives} + \text{Tips}$$ $$\text{Net In-Pocket Pay} = \text{Gross Earnings} - (\text{Petrol/EV Charging} + \text{Bike Maintenance} + \text{Mobile Data Share})$$

Gig delivery partners working with quick-commerce and food delivery platforms (Swiggy, Zomato, Blinkit, Zepto, Dunzo) earn through a dynamic rate-card mechanism. Total gross payout combines order base pay, distance compensation, weather surges, restaurant waiting bonuses, and milestone incentives. Real net earnings are determined after subtracting out-of-pocket fuel costs, routine motorcycle maintenance, and mobile telecom data expenses.

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