Whether you are comparing home loan offers from banks, preparing a GST-compliant tax invoice for a client, or planning a 15-year mutual fund Systematic Investment Plan (SIP), understanding the underlying math helps you verify every figure with confidence. Below are the exact formulas and worked examples used by our EMI Calculator, GST Calculator, and SIP Calculator.
1. Reducing-Balance Loan EMI Formula & Example
Banks calculate Equated Monthly Installments (EMI) for home, car, and personal loans on a monthly reducing-balance basis:
- P (Principal): Loan amount borrowed (for example, ₹5,00,000).
- r (Monthly Interest Rate): Annual interest rate divided by 12 and by 100 (for example, 8.75% per annum =
8.75 / 1200 = 0.0072917). - n (Tenure in Months): Total monthly installments (for example, 5 years =
60 months).
Worked Example: On a ₹5,00,000 loan at 8.75% for 60 months, your monthly EMI is ₹10,319, total repayment over 5 years is ₹6,19,117, and total interest paid is ₹1,19,117. You can test different tenures instantly on the EMI Calculator.
2. Forward (Exclusive) vs. Reverse (Inclusive) GST Calculation
One of the most common billing mistakes happens when removing GST from a GST-inclusive Maximum Retail Price (MRP). Subtracting 18% directly from the gross total gives the wrong number—you must divide by (1 + GST% / 100):
| Scenario | Formula | Example (₹11,800 at 18% GST) |
|---|---|---|
| Add GST (GST Exclusive) | Tax = Net × (R / 100)Gross = Net + Tax | Net ₹10,000 + ₹1,800 GST (₹900 CGST + ₹900 SGST) = ₹11,800 Gross |
| Remove GST (GST Inclusive) | Net = Gross / (1 + R / 100)Tax = Gross − Net | ₹11,800 / 1.18 = ₹10,000 Net Base Price and ₹1,800 GST |
3. Mutual Fund SIP Compounding Formula
Because each monthly SIP installment is invested at the start of the period and compounds monthly, the future maturity value (M) is calculated as:
For example, investing ₹5,000 per month at an expected 12% annual return (i = 0.01) for 10 years (`120` months) invests ₹6,00,000 of your own capital and generates an estimated ₹5,61,695 in compounded wealth gain, reaching a total maturity value of ₹11,61,695. Try your own monthly target on the SIP Calculator.