Loan Payment Calculator

How to use the loan payment calculator

Enter the loan amount, the annual interest rate as a percent, and the term in years, and the payment appears immediately. The defaults stand in for a common case: a $25,000.00 loan at 6.5% over 5 years comes to $489.15 a month. Underneath that you get the total paid, $29,349.22, and the total interest, $4,349.22.

Those last two are the numbers that decide whether a loan is a good one, and they are the numbers a sales conversation tends to skip past.

Drag the term slider or retype any field and all three update at once, so you can feel how each input pushes the cost around before you commit to anything. Nothing you type leaves the page, and the arithmetic is the same fixed-rate amortisation a lender uses.

This is a generic installment-loan calculator, the maths behind an auto loan, a personal loan, or a student loan. It assumes a fixed rate and equal monthly payments for the life of the loan, which is how those loans are normally written. It also models principal and interest only, so an origination fee deducted from your proceeds, a documentation fee, or credit insurance sold alongside the loan will not appear here unless you add them to the amount you enter.

There are only two levers worth testing, and it helps to move them one at a time. Cutting the rate from 6.5% to 5.5% on the same five-year loan drops the payment to $477.53 and the total interest to $3,651.74, a saving of $697.48 for a change you might get simply by shopping a second lender. Cutting the term does something different.

One number the calculator cannot show you is the APR, and it is worth knowing why they differ. Under Regulation Z, which implements the US Truth in Lending Act, the annual percentage rate expresses the whole finance charge as a nominal yearly rate, and the finance charge under 12 CFR 1026.4(a) is the cost of consumer credit as a dollar amount, including interest, points, loan fees, and any credit insurance required as a condition of the loan.

So a loan quoted at 6.5% with a two-point origination fee carries an APR above 6.5%, and it is the APR, not the note rate, that lets you compare two offers honestly. Regulation Z also allows a tolerance: a disclosed APR counts as accurate within one eighth of one percentage point on a regular transaction.

Where each payment actually goes

The payment never changes, but what each one buys does. Interest is charged on the outstanding balance, and that balance is largest at the start, so the first payment splits $135.42 to interest and only $353.74 to principal. The sixtieth reverses it almost completely: $2.64 interest and $486.52 principal.

After twelve payments you have handed over $5,869.84 and the balance has only fallen to $20,626.38, because $1,496.23 of that went to interest. By payment twenty-four the cumulative interest is $2,699.55, so 62 percent of the loan total interest is paid in the first 40 percent of the term.

The formula, worked line by line

A fixed-rate loan uses the standard amortisation formula: one level payment that exactly retires the balance over n periods, with nothing left over and nothing owing at the end. The single thing to get right is that r in the formula is the PERIODIC rate, not the annual one. For a monthly loan that means dividing the quoted annual rate by twelve before it goes anywhere near the exponent, and converting the term from years into months to match.

That conversion is where hand calculations fail. Feed the annual rate straight in and the formula still returns a number, just a badly wrong one, because it now believes you are paying 6.5% every month rather than 6.5% a year. The two inputs have to describe the same period as each other, and both have to describe the same period as the payment.

i = annual rate ÷ 12 ÷ 100      n = years × 12
payment = P × i × (1 + i)^n ÷ ((1 + i)^n − 1)      (if i = 0 → P ÷ n)
total paid = payment × n      total interest = total paid − P
$25,000 at 6.5% over 5 years: i = 0.0054167, n = 60 → $489.15

The rate and the term are not interchangeable levers. Dropping the rate to 5.5% saves $697.48 in interest and lowers the payment at the same time, which is the only change that improves both numbers at once.

Stretching the term to ten years lowers the payment further, to $283.87, but more than doubles the interest to $9,064.39. One lever makes the loan cheaper, the other only makes it easier to carry, and the difference between those two things is the whole art of comparing loan offers.

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