Instrument 07 · Borrow
Loan Amortization & EMI Calculator The Price Of Money, Month By Month.
A loan's monthly payment (EMI) is P × i ÷ (1 − (1 + i)^−n), where P is the amount borrowed, i the monthly rate (annual rate ÷ 12) and n the number of months. $20,000 at 7% over five years is $396.02 a month and about $3,761 of interest. An extra $100 a month saves $893.74 and 13 months.
Runs in your browserNothing uploaded or storedLast reviewed
The nominal rate from the loan offer, not an APR that folds in fees.
Up to 40 years.
Applied entirely to principal. The payment stays the same and the loan ends sooner.
Monthly payment (EMI)
Arithmetic in whole cents: the payment and each month’s interest are rounded half-up, and the final payment settles the balance exactly.
| Year | Paid | Interest | Principal | Balance after |
|---|
Every month
| Month | Paid | Interest | Principal | Balance after |
|---|
Reading Your Result
What The Number Is Telling You.
- Interest under 10% of the total
- Short or cheap borrowing.
- 10–30%
- A typical consumer or car loan.
- Above 30%
- Long or expensive borrowing — a 30-year mortgage at 6.5% pays more in interest than it borrowed.
The Model
The Formula, In Full.
The arithmetic this instrument runs, with a worked example. Its test cases are published on the methodology page
i = annual rate ÷ 12
Payment = P × i ÷ (1 − (1 + i)^−n); when i = 0: P ÷ n
Each month: interest = balance × i; principal = payment + extra − interest; balance −= principalWorked example. 20,000 at 7% for 60 months → 396.02 a month, 3,761.48 interest (cent-rounded schedule). Extra 100 a month → 47 payments, 2,867.74 interest. 250,000 at 6.5% for 360 months → 1,580.17 a month, 318,861.58 interest.
Assumptions and edge cases
- Fixed rate for the whole term; interest calculated monthly on the outstanding balance.
- The rate entered is the nominal annual rate, not an APR that includes fees.
- Extra payments go entirely to principal and shorten the term; the payment stays the same.
| Edge case | Behaviour |
|---|---|
| Rate 0% | Payment = amount ÷ months; the last payment absorbs rounding (10,000 over 24 = 416.67, last 416.59). |
| Extra ≥ remaining balance | The loan clears that month; the schedule stops. |
| Term outside 1–480 months | Rejected with a message; nothing computed. |
| Very long, high-rate loans | Totals formatted without overflow at every width. |
Questions
Loan Amortization & EMI, Answered Plainly.
How is a monthly loan payment (EMI) calculated?
The payment is P × i ÷ (1 − (1 + i)^−n), where P is the amount borrowed, i is the monthly interest rate (the annual rate divided by 12) and n is the number of monthly payments. The formula sets one fixed payment that covers each month's interest and repays the principal exactly by the final month. EMI stands for equated monthly instalment, the term used in South Asia for the same payment.
What is an amortization schedule?
An amortization schedule is the month-by-month table of a loan: each payment, how much of it is interest, how much repays principal and the balance left afterwards. It shows something a single monthly figure hides — early payments are mostly interest, and the share going to principal grows every month. The schedule above can be read by year or opened to every month.
Why is most of my early payment interest?
Interest is charged on the outstanding balance, and the balance is largest at the start. On a 250,000 mortgage at 6.5 per cent, the first month's interest alone is about 1,354 of a 1,580 payment. As principal is repaid, each month's interest falls and more of the same payment reduces the balance. Extra payments early in the loan save the most, for exactly that reason.
How much do extra payments save on a loan?
More than the extra itself, because every unit of principal repaid early stops accruing interest for the rest of the term. On 20,000 at 7 per cent over five years, an extra 100 a month saves 893.74 in interest and finishes 13 months early. On a 250,000 mortgage at 6.5 per cent, an extra 200 a month saves about 97,600 and nearly eight years.
What is the difference between APR and the interest rate?
The interest rate is the cost of borrowing the principal. The APR — annual percentage rate — adds certain fees and charges to express the total yearly cost of the loan, so it is usually higher. This calculator uses the nominal interest rate, which is what determines the monthly payment. Use the APR to compare offers from different lenders.
Should I choose a shorter or a longer loan term?
A shorter term means a higher payment and much less interest; a longer term means a lower payment and much more interest. On 20,000 at 7 per cent, three years costs 617.54 a month and 2,231.50 of interest, while seven years costs 301.85 a month and 5,355.80. Choose the shortest term whose payment still leaves your budget and emergency fund intact.
Does paying extra reduce my payment or my loan term?
Usually the term. Most lenders keep the payment fixed and apply extra money to principal, so the loan ends sooner, which is how this calculator models it. Some lenders can recast the loan to lower the payment instead, and some apply extra money to the next payment unless you mark it as principal only — check how yours treats it.