RightFiguresPrincipal and interest only
The regular payment is the standard annuity:
M = P × r / (1 − (1 + r)^(−n))
P is the loan amount, r is the annual rate divided by 100 and then by 12, and n is the number of months. At a 0% rate, M = P / n. In the calculation, that formula uses a positive power so a value that lands on a half cent is not nudged down.
M rounds half up to the nearest cent, and it is at least one cent. Each month’s interest is the remaining balance times the annual rate, divided by 1,200, then rounded half up to the cent. The last payment is whatever principal and interest remain, so it can be a few cents higher or lower than the regular payment. Totals add those actual payments. The balance ends at $0.00. A tiny balance can pay off before the last scheduled month; the page says when that happens.
If that last payment would be more than twice the regular payment, the calculator rejects the inputs and shows no result. Regulation Z § 1026.37(b)(5) uses that same line for a balloon payment. A term of one month is still the single installment you asked for.
This is not a disclosure APR
Dividing the rate you type by 12 is the convention this page states. It is not a lender’s Truth in Lending APR. Regulation Z § 1026.18 lists what a closed-end disclosure covers, including the annual percentage rate, the amount financed and the finance charge. The Consumer Financial Protection Bureau’s explanation of interest rate versus APR is about why those two numbers can differ. This page does not rebuild either one, and it does not add fees or insurance.
A personal installment loan is one use of this estimate. A car purchase that starts from price, tax and fees belongs on the car loan calculator. A home loan’s housing payment belongs on the mortgage payment calculator.
An $8,000 example
$8,000.00 at 9% for 48 months has a regular payment of $199.08. The final payment is $199.07. Total interest is $1,555.83, and the payments add to $9,555.83.
The same shape at 0% does not always split into equal cents. $25,000.00 at 0% for 60 months has a regular payment of $416.67 and a final payment of $416.47, and the payments still add to $25,000.00.
$100.00 at 100% for 120 months is rejected. The regular cent payment would not amortize the loan, and the last installment would be more than twice that payment. $500.00 at 12% for one month is a single payment of $505.00.
What this leaves out
There is no origination fee, no credit insurance, and no rate that changes. The term is 1 to 360 whole months. A payment you already have from a lender is not solved backward into an APR here.
Frequently asked questions
Is the rate I type the contract rate or a Truth in Lending APR?
Type the annual rate you want divided by 12. A disclosed APR can treat fees differently. This page does not rebuild that disclosure.
Why is the last payment different?
The regular payment is rounded to a cent. The last payment pays the remaining
balance and that month’s interest. If it would be more than twice the regular
payment, the estimate stops instead of showing a balloon.
Are the amount and rate sent to analytics?
No. Analytics may record that this calculator ran. The amount, rate and
payment stay in the browser.
Sources & review
- What is a personal installment loan? — Consumer Financial Protection Bureau
- What is the difference between a mortgage interest rate and an APR? — Consumer Financial Protection Bureau
- Regulation Z § 1026.18, content of disclosures — Consumer Financial Protection Bureau
- Regulation Z § 1026.37(b)(5), balloon payment — Consumer Financial Protection Bureau
Last reviewed: . The formula is reproduced above so you can check the math independently.
Educational estimate only. A lender’s payment, APR disclosure and fee list can differ.