Lesson 7 of 25 · 6 min

ARM reset arithmetic

A reset recomputes the installment on the remaining balance for the months that are left.

A reset is a new substitution into the installment formula. P is no longer the original principal. It is the remaining balance. n is no longer 360. It is the months that are left. r is no longer the start rate. It is the capped index-plus-margin from lessons 5 and 6. The payment that comes out is a different cash figure.

remaining after k payments = P × ((1+r)^n − (1+r)^k) / ((1+r)^n − 1)

P: The original principal.
r: The monthly rate in force during those k payments.
n: The original term in months.
k: The number of payments already made.

Ilex Lending's $248,900 at 5.40 percent for 360 months has payment $1,397.65. After 60 payments the remaining balance is $229,827.56. The first reset writes 6.65 percent, which lesson 6 already showed sits inside the initial cap. Remaining term is 300 months. The new payment is $1,573.42. The rise is $1,573.42 − $1,397.65 = $175.77.

Nothing about the house moved. Nothing about the original $248,900 moved except that sixty payments reduced it to $229,827.56. The $175.77 is the cash consequence of a new r on a still-large P over a still-long n. Track 1 lesson 13's formula did this on a calendar the loan itself wrote: month 60, not the week the index printed 3.90 percent.

A reset does not restart the loan. It re-solves the installment on what is left, at the new rate, for the months that remain.

Key terms

Reset: The scheduled date on which r is rewritten from index plus margin, inside the caps, and the installment is recomputed.
Remaining term: Months left after the reset. Here, 360 − 60 = 300.
Payment step: New installment minus old installment. Here, $175.77.

Worked example

Month 60, a new substitution

Ilex Lending. Original $248,900 at 5.40 percent for 360 months. After 60 payments, reset to 6.65 percent for 300 months.

Payment, months 1–60: $1,397.65
Remaining balance at month 60: $229,827.56
New r: 6.65%
New payment: $1,573.42
Rise: $175.77

The house did not change. The remaining $229,827.56 at a new r produced $175.77 more cash a month.

Check yourself

Principal $186,500 at an illustrative 5.15 percent for 360 months, payment $1,018.34. After 60 payments the remaining balance is $171,621.68. Reset to 6.40 percent for 300 months. What is the new payment, and what is the rise?

An ARM reset is a variable rate moving by index plus spread, limited by the caps — Track 1 lesson 13's formula on a calendar the loan itself wrote. Open Variable rates: how index plus spread works →

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.