Loan Lifecycle Planner Refi Payoff

A fully amortizing loan payment is the constant monthly cash flow whose present value, discounted at the periodic rate, equals the outstanding principal. That is why the payment formula is simply the annuity present-value expression inverted: r is the nominal annual rate divided by 12 and n is the number of monthly payments remaining. Because interest is charged each month on the balance still owed, early payments are dominated by interest. On a balance of 250,000 dollars at 6.5 percent with 25 years left, the payment is about 1,688 dollars, of which roughly 1,354 is interest and only 334 reduces principal in month one. Refinancing swaps that payment stream for a cheaper one, and rolling closing costs into the new balance makes the refinanced principal larger than the old. The standard test divides closing costs by the monthly payment reduction to get a breakeven month count. Closing costs typically run 2 to 5 percent of the loan, and lenders often cite a 0.75 to 1.0 percentage point rate drop as a minimum. Two caveats matter: resetting to a fresh 30-year term can raise lifetime interest even when the rate falls, and this model assumes a fixed rate held to maturity with no mortgage insurance, tax effects, or cash-out.

The arithmetic of level payments predates mortgages by centuries. Richard Witt's Arithmeticall Questions of 1613 is among the earliest English treatments of compound interest and annuity valuation, and commercial annuity tables circulated widely across Europe well before consumer lending existed. The self-amortizing home loan itself is much newer. Before the 1930s, American mortgages were commonly short-term interest-only balloon notes of three to five years that had to be rolled over at maturity. The wave of defaults during the Great Depression prompted the Home Owners Loan Corporation in 1933 and the Federal Housing Administration in 1934, both of which promoted the long-term, fixed-rate, fully amortizing loan that made these tables a household calculation. Refinancing became a mass behavior once rates were observable and transaction costs fell. Freddie Mac has published its Primary Mortgage Market Survey of average 30-year fixed rates weekly since 1971, and the Mortgage Bankers Association has tracked refinance application volume since 1990, showing distinct surges in 1993, 1998, 2003, 2012, and again in 2020 and 2021 when 30-year rates fell below 3 percent. Rules of thumb such as the two-point rule were later formalized: Agarwal, Driscoll, and Laibson published a closed-form optimal refinancing threshold in the Journal of Money, Credit and Banking in 2013, showing that simple rules often mistime the decision.