Calculator Assumptions

Use this form to calculate the periodic repayment of borrowed principal and interest incurred for a given time period and interest rate. The assumption of this calculator is that the regular payments (consisting of principal and interest) are equal, and that the first installment is due one payment interval after the borrowing date. There may be one balloon payment which is assumed to occur one payment interval after the final regular payment. (Exempli gratia, a one-year loan repaid in monthly installments and a final balloon payment would consist of 11 regular payments and one balloon payment.) The balloon payment also consists of principal and interest parts.

If you request an amortization schedule be shown, you can see how the principal and interest vary from payment to payment. There may be small discrepancies between the amortization schedule and the summarized calculations above the schedule. In calculating the schedule, principal and interest parts are rounded to the nearest penny, while the summary calculations above the schedule come directly from the analytic equation for amortization that I derived. Your lending institution may use a different method of handling fractional pennies. The final payment (or balloon payment) of the amortization schedule is adjusted (up or down) so that the debt is liquidated entirely.

If you are buying real estate, be sure that the loan amount (principal) is sale price of the property less the down payment. For example, property with a sale price of $100,000 which you might buy with 10% down ($10,000) would require a loan of $90,000.

Nota Bene: The payment amount for this calculator will only include principal and interest. But it doesn't stop there if you are trying to determine what your monthly payment will be when buying real estate. In addition to P&I, other money may be collected regularly by the bank or mortgage company to meet future payments of property taxes, mortgage insurance, homeowner's insurance, or other fees. This escrow payment is added on top of the monthly P&I, and is usually independent of the terms of the loan. Depending on the bank, you may be assessed a one-time escrow management fee at closing.

See common questions and answers in the FAQ.

My Derivation

For the math inclined, I have written down my derivation of the amortization equation. There's also a document which shows how to calculate with a moratorium before the payment schedule begins, and how to calculate an earlier payoff value. If you're trying to figure out the original parameters of an amortization schedule, maybe the math on obtaining the payment and interest rate will be helpful to you. If your curious about recent changes to the calculator, you may want to read my blog, or instead, you may wish to return to my home page, or you may want to e-mail me (bret at met dot fsu dot edu) about this program.


In early days of the personal computer industry, I finished college with a degree in Computer Science. I financed some of my education and living expenses using credit cards (not wise, but it got me through), and once I had a job, I wanted to know how long it would be before I could liquidate my high-interest debts. The web didn't exist then, so I went to the library first to look up equations for amortization. (Much as I love books, it's harder to find things in them quickly, compared to the web, especially since I wasn't really sure what I was looking for and didn't know the lingo.)

After some unsuccessful digging, I decided that I could probably put to use some of the math I'd learned as requirements for my freshly-minted CompSci degree, and I sat down to figure out the problem. (So almost certainly, the math you'll find in the derivation above isn't how the finance industry would describe things, but the basic principles are the same.) Once the math was done, the program quickly followed. Since my first question was "how long will I pay?", not "how much will I pay?", the program was designed with that flexibility in mind. With the program completed, I had a nice little tool that helped to guide me out of credit card hell.

Skipping ahead to the 90s, the World Wide Web was in its nascent stages, and techno-geeks were starting to assert their presence in cyberspace. I began putting together my own personal biographical babble, and thought about what I could offer website visitors that might be useful. I immediately thought of the calculator, and I re-wrote it to work with web protocols. Though I personally found the calculator useful, I never thought of it as anything more than a web curiosity.

Eventually I started receiving e-mail from people who were using the calculator: asking questions, asking for additional features, or just saying "thanks" for putting it out there, and I was gratified. When search engines came along, my little calculator started getting more and more use, and for some reason, it continued to be ranked highly.

Until 2008, the calculator ran on a webserver in the Meteorology Department at Florida State University where I work. Since the university's function is to provide information and research to students and the world at large, running the calculator using university resources was not at conflict with our institutional mission (though one would certainly question what it has to do with Meteorology :-). However, the server on which the calculator had been running for over a decade was being decommissioned, and the calculator had to move. Since the calculator gets a LOT more use now than when it was first launched, I could no longer justify putting it on a new department webserver, so I moved it to this off-campus website.

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