Solve for monthly payment, loan amount, or term given any two of the three variables.
Choose what you want to solve for — the monthly payment, the loan amount a payment can support, or how many months (term) it takes to repay — then fill in the other values.
All three use the same fixed-rate amortization equation with monthly payments; a 0% rate is supported.
Payment: M = P × r / (1 − (1 + r)^−n)Loan amount: P = M × (1 − (1 + r)^−n) / rTerm: n = −ln(1 − P·r / M) / ln(1 + r)r = annual rate ÷ 12. When r = 0: M = P ÷ n.
Use M = P × r / (1 − (1 + r)^−n), where P is the loan amount, r is the annual interest rate divided by 12, and n is the number of monthly payments. For example, $10,000 at 6% over 60 months is about $193.33 a month.
Rearrange the payment formula: P = M × (1 − (1 + r)^−n) / r. Pick “Find loan amount”, enter the payment you can afford, the rate and the term, and the calculator returns the maximum loan.
If the payment is less than or equal to the monthly interest on the balance, the balance never falls. Increase the payment above the first month’s interest (loan × annual rate ÷ 12) to make progress.
Yes — this calculator finds the required payment, the loan amount a payment supports, or the number of payments. To solve for the interest rate, use the Interest Rate calculator.
Every loan payment consists of two parts: interest (the cost of borrowing) and principal (repaying the borrowed amount). In the early years of a loan, most of each payment goes toward interest. As the balance decreases, more goes toward principal. This is why extra payments early in the loan have the biggest impact on total interest saved.
Did you know?
The 28/36 rule is a widely used guideline: your monthly housing costs should not exceed 28% of gross monthly income, and total debt payments should stay below 36%.
Monthly payment calculations use the annuity formula developed in the 17th century. The concept of equal periodic payments to repay a debt was formalized by mathematicians studying actuarial science and life insurance, leading to the standardized amortization tables used by banks worldwide today.
Making bi-weekly payments instead of monthly results in 26 half-payments (13 full payments) per year, effectively making one extra payment annually.
Even small extra payments toward principal can dramatically reduce total interest. An extra $100/month on a $200,000 mortgage saves over $30,000 in interest.
Payment calculators use the same time-value-of-money formula used by banks and financial institutions worldwide.