The maths, with your numbers
What paying extra would do
Every dollar above the payment comes straight off the balance, so the interest stops being charged on it. These are worked out from the loan above.
How the balance falls
The same loan over different terms
| Term | Payment | Total interest | Total repaid |
|---|
A longer term lowers the payment and raises the interest. Your loan is highlighted.
Amortization schedule
Where each payment goes, from the first to the last.
EMI stands for equated monthly instalment: the same amount paid every month until the loan is gone. It is the standard term in India for what Americans simply call a loan payment, and the arithmetic is identical.
The boxes above show a dollar sign, but the formula does not care about the currency. Enter your amount in rupees and read the instalment in rupees.
The formula
EMI = P × i × (1 + i)n ÷ ((1 + i)n − 1), where P is the principal, i is the monthly rate and n is the number of months. That is the same annuity formula the calculator above uses, written a different way. Enter your amount, rate and term and it gives the instalment, the total interest and the full schedule.
What moves an EMI
- A floating rate. On a floating-rate loan the lender resets the rate periodically. The Reserve Bank of India requires lenders to let borrowers choose between a higher instalment, a longer tenor, or a mix, and to be told at the outset what a rate change would do.
- The tenor. A longer tenor lowers the instalment and raises the total interest, as the term table above shows.
- Prepayment. Paying extra reduces the principal and either shortens the tenor or lowers future instalments, depending on what you ask for.
Reading a loan statement
Indian lenders must give borrowers a quarterly statement showing the instalment, the number of instalments left and the annual percentage rate for the whole tenor. That last figure is the one to compare between lenders, for the same reason APR is the right comparison in the United States.
Quick answers
What is EMI?
Equated monthly instalment: the fixed amount paid every month on a loan, covering interest and principal. It is the standard term in India for a loan payment.
What is the EMI formula?
EMI = P x i x (1+i)^n / ((1+i)^n - 1), where P is the principal, i the monthly rate and n the number of months. It is the same formula as a US amortizing payment.
Does prepaying reduce the EMI or the tenor?
Either, depending on what you ask the lender for. Reducing the tenor saves more interest; reducing the instalment frees up monthly cash.
What happens when a floating rate changes?
The Reserve Bank of India requires lenders to offer a choice between a higher instalment, a longer tenor, or a mix, and to explain the effect at the outset.
Sources
- Reserve Bank of India, reset of floating interest rates on EMI-based personal loans (2023)
- 12 CFR § 1026.22, the equivalent US rule on disclosed rates