Refinancing break-even, as arithmetic

Refinancing, the writing of a new loan that retires the old one, has a break-even that is the same identity as lesson 10's points: prepaid cost divided by monthly difference. A new loan also resets amortization. The remaining balance becomes a new P, often with a new n, so the principal-and-interest split starts interest-heavy again, the way lesson 2's first month did. Other terms can reset with it: a margin, a prepayment clock, an insurance line. This lesson is the identity. It does not choose the new loan.

Kestrel Home Finance's old payment is $2,148.30. The new payment is $1,894.12. Closing costs, the prepaid cash of writing the new loan, are $6,420. Monthly saving is $2,148.30 − $1,894.12 = $254.18. Break-even is $6,420 ÷ $254.18 = 25.26 months. Twenty-six months of $254.18 is $6,608.68, which first exceeds the $6,420.

Track 1 lesson 13's spread, paid another way, is the mechanism. Points paid a spread on day one for a lower r on the same P. Closing costs pay a fee on day one for a different r, and often a different P and n, on a replacement loan. The division is the same shape. The objects being divided are a fee and a monthly difference. The quotient is a count of months, not a verdict.

Because amortization resets, the $1,894.12 is not the old loan with $254.18 knocked off. It is a new substitution. Remaining term may lengthen. A later remaining-balance row is not the old schedule continued. Break-even counts cash against cash. It does not hold the old principal-retired path still.

Break-even is an identity. A new loan is a new P, a new r, a new n, and a reset clock. The identity does not recommend the replacement.