This payment calculator works in two directions. Solve for the monthly payment when you know the loan amount, interest rate, and term — or flip it around and solve for the loan term when you know how much you can afford to pay each month.
The second mode answers a question lenders rarely show you: “If I pay $X per month, when will this debt be gone?” It is especially useful for credit card payoff planning and for testing how larger payments shorten a loan. Both modes report total interest, so you can see the real cost of any repayment plan.
The Math in Both Directions
Solving for the payment uses the standard amortization formula:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
Solving for the term rearranges the same equation to isolate n:
n = −ln(1 − rP/M) / ln(1 + r)
Where P is the loan amount, r is the monthly rate (APR ÷ 12), M is the monthly payment, and n is the number of months.
The term formula has a hard requirement: M must be greater than the first month’s interest (P × r). If your payment only covers interest, the balance never shrinks and n is infinite — mathematically, the logarithm’s argument goes to zero or negative.
How Payment Size Changes Payoff Time
Payoff time responds non-linearly to payment size — small increases near the minimum have outsized effects. On a $20,000 loan at 6% APR (first month’s interest: $100):
- $150/month: about 220 months (18.4 years), roughly $13,040 interest.
- $250/month: about 102 months (8.5 years), roughly $5,605 interest.
- $400/month: about 57.7 months (4.8 years), roughly $3,072 interest.
- $600/month: about 36.6 months (3 years), roughly $1,933 interest.
Going from $150 to $250 — just $100 more — cuts payoff time by more than half and saves over $7,400 in interest. This is why paying meaningfully above the minimum on credit cards matters so much.
Example: Solving Both Ways at $20,000 and 6%
Payment mode: borrow $20,000 at 6% APR for 5 years. The monthly rate is 0.5%, n = 60, and the formula gives a payment of about $386.66. Total repaid is roughly $23,199, of which $3,199 is interest.
Term mode: same loan, but you decide to pay $400 per month. Then n = −ln(1 − 0.005 × 20,000 ÷ 400) / ln(1.005) = −ln(0.75) / ln(1.005) ≈ 57.7 months — about 4 years 10 months, with roughly $3,072 in total interest.
The extra $13 per month over the 5-year payment saves about $127 in interest and finishes the loan 2 months sooner.
Frequently Asked Questions
How do I calculate a monthly loan payment?
Use M = P × [r(1 + r)^n] / [(1 + r)^n − 1], where P is the loan amount, r is the monthly interest rate (APR divided by 12), and n is the number of monthly payments. For a $20,000 loan at 6% over 5 years, that works out to $386.66 per month.
How long will it take to pay off my loan at a fixed monthly payment?
The number of months is n = −ln(1 − rP/M) / ln(1 + r), where P is the balance, r is the monthly rate, and M is your payment. Paying $400 monthly on $20,000 at 6% takes about 58 months. Your payment must exceed the monthly interest for payoff to be possible.
Why does my payment have to be bigger than the monthly interest?
Each month, interest is charged on the remaining balance. If your payment only covers that interest, nothing reduces the principal, so the balance — and next month’s interest — never shrinks. On $20,000 at 6%, the first month’s interest is $100, so any payment of $100 or less can never pay off the loan.
Does paying more per month save interest?
Yes, and the effect compounds. Every extra dollar reduces principal immediately, which lowers all future interest charges. On a $20,000 loan at 6%, raising the payment from $250 to $400 cuts payoff time from 8.5 years to 4.8 years and saves about $2,533 in interest.
What is the difference between this and an amortization calculator?
A payment calculator solves for one unknown — the payment or the term — while an amortization calculator takes all inputs as given and produces the full payment-by-payment schedule showing principal, interest, and balance over time. Use this tool to size the loan, then view the schedule.