Calxsolver
Finite Math

Loan Payment Calculator

From the principal, APR, term and payment frequency the calculator derives the periodic rate r = APR/m, the number of payments N = m·t, the level payment PMT = P·r / (1 − (1 + r)⁻ᴺ), the total paid and the total interest, with a preview of the first amortization rows.

Loan Payment Calculator

Periodic payment, total interest and a first-rows amortization preview.

Try:
AnswerPayment = 1073.64 per period; total interest 186511.57
  1. PrincipalP = 200000.00
  2. APR5%
  3. Term30 years, 12 payments per year (360 total)
  4. Periodic rater = 5% / 12 = 0.416667% per period
  5. FormulaPMT = P · r / (1 − (1 + r)⁻ᴺ)
  6. PaymentPMT = 1073.64 per period
  7. Total paid386511.57 = 360 · 1073.64
  8. Total interest186511.57
  9. Payment 1interest 833.33, principal 240.31, balance 199759.69
  10. Payment 2interest 832.33, principal 241.31, balance 199518.38
  11. Payment 3interest 831.33, principal 242.32, balance 199276.06
  12. Payment 4interest 830.32, principal 243.33, balance 199032.74
Report an error

Worked examples

Monthly payment on a $200,000 mortgage at 5% for 30 years Find the level payment and total interest on an amortized loan.

Frequently asked questions

What does APR mean?

APR is the annual percentage rate — the nominal yearly rate. The calculator divides it by m to get the periodic rate used in the payment formula.

Why does the early payment go mostly to interest?

Each period interest is charged on the remaining balance. Early on that balance is large, so most of the level payment covers interest and only a small slice reduces principal.

Can I model bi-weekly payments?

Yes. Set m to 26 and divide the term accordingly. Bi-weekly schedules tend to reduce total interest because of more frequent compounding.

Related solvers

Simple Interest Calculator I = Prt — find interest and the final amount on a flat-rate loan or deposit. Compound Interest Calculator A = P(1 + r/n)^(nt) for discrete compounding, A = Pe^(rt) for continuous. Annuity Calculator Future value or present value of an ordinary annuity from payment, rate and periods. Markov Chain Calculator Iterate the distribution and find the steady-state vector π. Linear Programming Solver (2 variables) Graphical method — feasible region, corner-point evaluation and the optimum. Truth Table Generator Build a truth table for any propositional formula over p, q, r, s.