The payment for a fixed term
For a fixed-rate loan repaid in equal monthly installments, the payment depends on three things: the amount, the rate and the number of payments. The formula is payment = P × r(1 + r)^n ÷ ((1 + r)^n − 1), with r the monthly rate. Doubling the amount doubles the payment; stretching the term lowers it, but by less each time, because more of each payment becomes interest.
| Amount | 2 years | 3 years | 5 years | 7 years |
|---|---|---|---|---|
| $5,000 | $221.60 | $152.11 | $96.66 | $73.04 |
| $10,000 | $443.21 | $304.22 | $193.33 | $146.09 |
| $20,000 | $886.41 | $608.44 | $386.66 | $292.17 |
| $30,000 | $1,329.62 | $912.66 | $579.98 | $438.26 |
| $50,000 | $2,216.03 | $1,521.10 | $966.64 | $730.43 |
How long a fixed payment takes
Run the other way, the question is how many months a payment of a given size needs. Solving the same formula for n gives n = −ln(1 − P × r ÷ PMT) ÷ ln(1 + r). If the payment does not exceed the first month's interest the balance never falls, which the calculator reports rather than returning nonsense. The last payment is smaller than the others, since it only has to clear what remains.
| Monthly payment | Time to pay off | Total interest | Total paid |
|---|---|---|---|
| $300.00 | 6 yr 9 mo | $4,389 | $24,389 |
| $400.00 | 4 yr 10 mo | $3,072 | $23,072 |
| $500.00 | 3 yr 9 mo | $2,370 | $22,370 |
| $750.00 | 2 yr 5 mo | $1,519 | $21,519 |
| $1,000.00 | 1 yr 9 mo | $1,125 | $21,125 |
How the rate moves the payment
Rate matters less than most people expect for the payment itself on a short loan, and more for the total interest. Over five years on $20,000, each percentage point adds roughly $9 a month but about $550 in total interest.
| Rate | Monthly payment | Total interest |
|---|---|---|
| 3% | $359.37 | $1,562 |
| 5% | $377.42 | $2,645 |
| 6% | $386.66 | $3,199 |
| 8% | $405.53 | $4,332 |
| 10% | $424.94 | $5,496 |
| 12% | $444.89 | $6,693 |
| 15% | $475.80 | $8,548 |
| 20% | $529.88 | $11,793 |
Choosing a payment you can sustain
A lower payment always means more interest, because the balance stays outstanding longer. The useful discipline is to pick the shortest term whose payment fits the budget with room to spare, then treat any extra as optional prepayment rather than committing to a payment that only fits in a good month. Lenders size loans on debt-to-income ratios; a payment that keeps total debt payments under about 36% of gross income is the conventional ceiling.
Amortization schedule and payoff date
Below the result, the yearly and monthly schedules show every payment split into interest (balance × monthly rate) and principal (payment − interest), with the balance after each payment. Both download as CSV. The last payment is trimmed so the balance lands exactly on zero.
Enter the first payment month as YYYY-MM (it defaults to the current month). The payoff date is the first payment month + (n − 1) months. Example: $20,000 at 6% paid at $400 a month takes 58 payments, so a loan whose first payment is in October 2026 is paid off in July 2031.