How to use the payment calculator
This calculator answers two different questions about the same loan, so start by choosing a mode:
- Fixed term asks how much you will pay each month. Enter the loan amount, the annual interest rate and the term in years, months or both.
- Fixed payment asks how long repayment will take. Enter the loan amount, the annual interest rate and the monthly payment you plan to make.
Press Calculate to see the monthly payment, the time to pay off, the final payment, the total paid and the total interest. A yearly amortization schedule below the result shows how much interest and principal you pay each year and what you still owe at the end of it.
How it differs from a loan calculator
A typical loan calculator only works in one direction: you give it a term and it gives you a payment. Here you can also turn the question around. If your budget allows a set amount each month, the fixed payment mode tells you how many months that payment needs to clear the debt and how much interest you will pay along the way.
The formulas
With a monthly rate r (the annual rate divided by 12) and a loan amount P:
- Monthly payment for n months: M = P × r / (1 − (1 + r)^−n)
- Number of months for a payment M: n = −ln(1 − P × r / M) / ln(1 + r)
When the rate is 0%, the payment is simply P / n and the number of months is P / M. The number of months is rounded up to a whole month, and the last payment is smaller because it only clears what is left.
Worked example
A loan of 200,000 at 6% for 30 years has a monthly payment of 1,199.10. Over 360 payments you pay 431,676.38 in total, of which 231,676.38 is interest.
Now take a loan of 10,000 at 12% and a payment of 500 a month. The monthly rate is 1%, so n = −ln(1 − 100 / 500) / ln(1.01) ≈ 22.43. That means 22 full payments of 500 and a final payment of 213.48, or 1 year 11 months in total. The interest comes to 1,213.48.
Good to know
- Your payment must be larger than the first month's interest, otherwise the balance never goes down. The calculator tells you when that happens.
- Small increases to the payment can cut the payoff time sharply, especially when the rate is high.
- Results assume a fixed rate, payments at the end of each month and no fees. Lenders may round differently, so treat the figures as estimates.