Mathematical & Financial Formula Hub

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EMI Formula

$$EMI = P \times r \times \frac{(1 + r)^n}{((1 + r)^n - 1)}$$

An Equated Monthly Installment (EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. The EMI is structured to pay off both the interest and the principal balance of a loan over a set period. In the early stages of the loan, a larger portion of the monthly payment goes toward interest, while in later stages, more goes toward the principal. This amortization schedule helps borrowers plan their monthly budget and track their path to debt freedom.

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EPF / PF Calculation Formula

$$\text{EPF / PF Balance}_{t} = (\text{Balance}_{t-1} + \text{Emp}_{\text{12\%}} + \text{Empr}_{\text{3.67\%}}) \times \left(1 + \frac{r}{12}\right)$$

The Employee Provident Fund (EPF or PF) calculation formula computes monthly accumulation and annual interest crediting for organised sector employees in India under EPFO rules. Employees contribute 12% of Basic + DA, matched by a 12% employer contribution (split into 8.33% for Pension EPS capped at ₹1,250 and 3.67% into EPF / PF). Monthly contributions earn interest calculated monthly and credited annually at government-notified EPFO rates.

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Unit Converters

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Fahrenheit to Celsius Formula

$$°C = (°F - 32) \times 5/9$$

To convert Fahrenheit (°F) to Celsius (°C), subtract 32 from the Fahrenheit temperature and then multiply by 5/9 (or divide by 1.8).

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Finance

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FD Formula

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

A Fixed Deposit (FD) is a secure investment offered by banks and financial institutions where you deposit a lump sum for a fixed tenure at a guaranteed interest rate. FDs usually calculate compound interest on a quarterly basis. It offers steady, predictable growth on capital.

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Mathematics & Education

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Fraction Calculation Formulas

$$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}, \quad \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}, \quad \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$$

Fraction arithmetic rules govern addition, subtraction, multiplication, and division of rational numbers by finding common denominators or multiplying numerators and denominators directly.

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Mathematics & Education

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GPA Formula (Grade Point Average)

$$\text{GPA} = \frac{\sum (\text{Grade Points}_i \times \text{Credit Hours}_i)}{\sum \text{Credit Hours}_i}$$

Grade Point Average (GPA) is a weighted average calculation that measures academic performance by multiplying each course grade point value by its credit weight, summing the total quality points, and dividing by total credit hours attempted.

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Finance

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Gratuity Formula

$$Gratuity = \frac{15 \times Last\ Drawn\ Salary \times Service\ Years}{26}$$

Gratuity is a lump-sum payment made by an employer to an employee as a token of appreciation for services rendered, typically after completing 5 or more years of continuous employment.

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Tax

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GST Formula

$$\begin{aligned} \text{GST Amount} &= \text{Original Cost} \times \frac{\text{GST\%}}{100} \\ \text{Total Price} &= \text{Original Cost} + \text{GST Amount} \end{aligned}$$

Goods and Services Tax (GST) is a comprehensive indirect tax levied on the supply of goods and services. When computing transactions, you either add GST to find the final customer price, or subtract (remove) GST from the final retail price to find the pre-tax base cost.

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Home Loan Eligibility Formula

$$\begin{aligned} \text{Max EMI} &= (\text{Monthly Salary} \times \text{FOIR}) - \text{Existing EMI} \\ \text{Eligible Loan} &= \text{Max EMI} \times \frac{(1+r)^n - 1}{r(1+r)^n} \end{aligned}$$

Banks use the Fixed Obligation to Income Ratio (FOIR) method to decide how much of your monthly income can go toward loan repayments. The FOIR percentage itself rises with income (40% for lower incomes up to 55% for higher earners), reflecting that higher earners can comfortably commit more of their salary. Once the maximum affordable EMI is known, the eligible loan amount is reverse-calculated using the standard loan annuity formula.

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Tax

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HRA Exemption Formula

$$HRA\ Exempt = \min\left( \text{Actual HRA}, \text{Rent Paid} - 10\%\ \text{Basic}, 50\%\ \text{Basic\ (Metro)}\ \text{or}\ 40\%\ \text{Basic\ (Non-Metro)} \right)$$

House Rent Allowance (HRA) exemption is calculated under Section 10(13A) of the Income Tax Act. It determines the tax-exempt portion of the HRA received by salaried individuals living in rented accommodations.

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