A loan payment calculator finds one monthly installment that pays a principal down to zero over a fixed number of months, at one nominal annual rate. The rate is divided by 12 to get the monthly rate. That field is not a regulated APR, because an APR that includes fees would be a different number, and this page has no fee input.
The result is a payment, the number of payments, the total paid, and either interest or a rounding residual. Interest appears only when the rate is above zero. It is total paid minus principal, after the installment has been rounded to cents. At a zero rate the same cents difference is labeled rounding residual. It is not labeled interest. One payment at 0 percent returns the principal itself, and the residual is 0.00.
This page is not a mortgage calculator. It does not add taxes, insurance, escrow, points, or a balloon. Growing a balance forward is the other direction, on the Compound Interest Calculator. Do not read a future value on that page as a monthly installment, or this installment as a savings balance.
Enter in a field runs Calculate. A blank rate, a decimal payment count, and a principal of 0 are rejected. Clear removes the previous total.
Let P be the principal, n the number of monthly payments, and i the monthly rate (annual percent ÷ 100 ÷ 12). If the rate is 0, payment = P ÷ n. Otherwise payment = P × i × (1 + i)^n ÷ ((1 + i)^n − 1). The payment is rounded half away from zero to cents before anything else is totaled. Total paid = that rounded payment × n. When the rate is above zero, interest = total paid − principal. When the rate is 0, total paid − principal is the rounding residual.
Rounding the installment first is deliberate. A borrower pays the rounded amount, so the total should be that amount times the count, not an unrounded formula times the count. On 1000 at 0 percent over 12 payments, each installment rounds to 83.33, the total is 999.96, and the residual is −0.04. The minus sign means the rounded payments add up to four cents less than the principal. That line stays a rounding residual.
Principal 1000, rate 0, 1 payment: payment 1000.00, total 1000.00, rounding residual 0.00. Principal 1000, rate 0, 12 payments: payment 83.33, total 999.96, rounding residual −0.04. Principal 1000, rate 12 percent, 1 payment: payment 1010.00 and interest 10.00, because one month at 1 percent of 1000 is 10, and the figure is exact in cents. Principal 1000, rate 12 percent, 12 payments: the installment is 88.85, the total paid is 1066.20, and the interest is 66.20. Those last three numbers already include the cent rounding of the installment.
0% and 1 payment: payment = 1000
12% and 1 payment: payment = 1010.00The payment is computed in the browser. The principal you type is not uploaded, not stored, and not sent to a lender. This page does not pull a live rate. Clear the fields when you finish.
The rate is a nominal annual rate divided by 12. It is not a regulated APR that includes fees. The payment is rounded half away from zero to cents first, then multiplied by the number of payments. At a zero rate, the cents difference is a rounding residual, not interest. This is not a lender quote.
There is no interest at a zero rate. If the principal does not divide evenly into the payment count, rounding each installment to cents leaves a few cents over or under. That gap is the residual.
No. The field is a nominal annual rate, and the monthly rate is that percent divided by 12. Fees are not part of the formula.
Principal 1000 for 1 month at 12 percent a year is a 1 percent monthly rate, so the payment is 1010.00 and the interest is 10.00.
No. Those amounts are local and are not in this formula. The page calculates the installment on principal and rate only.