Finance calculators

Mortgage calculator

Monthly principal and interest, property tax, insurance and fees, total interest and a year-by-year amortisation chart.

Inputs

Results

Methodology

Conventions

  • Fixed rate, monthly payments; the nominal annual rate r is divided by 12.
  • Loan amount L = home price − down payment, repaid in n = 12 × term equal payments.
  • Property tax and insurance are spread evenly over 12 months and added to the monthly cost, with any monthly fees.

References

  • Kellison, The Theory of Interest, ch. 3 and 5

Formulas

Monthly payment
A = L \cdot \frac{i}{1 - (1 + i)^{-n}},\quad i = r/12
Interest in month k
I_k = B_{k-1} \cdot i,\quad B_k = B_{k-1} - (A - I_k)
Monthly cost
A + \frac{\text{tax} + \text{insurance}}{12} + \text{fees}
Loan to value
LTV = L / \text{price}