Amortization Schedule Calculator

An amortization schedule is the payment-by-payment solution to a single equation: the present value of n level payments discounted at the periodic rate r must equal the principal P. Solving for the payment gives M = P x r(1+r)^n / ((1+r)^n - 1), the ordinary annuity formula. Each period the lender first takes interest equal to the outstanding balance times r, and whatever remains of the fixed payment retires principal. Because the balance falls every month, the interest slice shrinks and the principal slice grows on a geometric path, which is why the split is so lopsided early on. On a 250,000 dollar loan at 6.5 percent over 360 months the payment is about 1,580.17 dollars, of which roughly 1,354 dollars is interest and only 226 dollars principal in month one; by the final year almost the whole payment is principal. The crossover point where principal first exceeds interest arrives late for long, high-rate loans - around year 18 of a 30-year loan at 6.5 percent, but before year 5 on a 15-year loan at the same rate. Total interest on that 30-year example runs about 318,900 dollars, roughly 128 percent of the amount borrowed. Two caveats matter when reading the table. First, the schedule shows principal and interest only; escrowed property tax, hazard insurance, HOA dues, and private mortgage insurance are additional and commonly add 300 to 800 dollars a month. Second, the schedule assumes exact monthly compounding and on-time payments. Any prepayment, late fee, rate reset on an adjustable loan, or a servicer that applies extra funds to future installments rather than principal will make the actual balance diverge from the projection.

Level-payment amortization rests on annuity mathematics developed for life contingencies. Edmond Halley published a method for valuing life annuities on the Breslau mortality data in 1693, and Richard Price systematized compound interest and reversionary payment tables in his Observations on Reversionary Payments of 1771. Through the nineteenth century, however, American home lending had almost nothing to do with these tools. Mortgages were typically short balloon instruments of three to five years, interest-only, requiring refinancing at maturity. Building and loan associations, beginning with the Oxford Provident Building Association founded near Philadelphia in 1831, were among the first to use share-accumulation plans that behaved like amortization. The fully amortizing long-term mortgage became the American standard through Depression-era policy. The Home Owners Loan Corporation, created in 1933, refinanced defaulted balloon mortgages into amortizing loans of up to 15 years, and the Federal Housing Administration, established by the National Housing Act of 1934, insured amortizing loans with 20-year and later 30-year terms and high loan-to-value ratios. The Federal National Mortgage Association followed in 1938 to buy those loans, and the 30-year fixed amortizing mortgage became the dominant product after the Second World War. Payment tables were computed by hand and published in books such as the Financial Publishing Company monthly payment volumes until pocket financial calculators, notably the Hewlett-Packard HP-80 of 1973 and the HP-12C of 1981, put the annuity formula directly in a loan officer's hand.