Lesson 5 of 25 · 6 min
How term length changes the payment
A longer schedule shrinks what leaves the account each month and leaves more of the claim still sitting on the car.
Stretching the term shrinks the installment and leaves more of the claim outstanding against the same car. The principal does not change. The rate does not change. What changes is n, the number of months over which that principal is spread, and the formula answers with a smaller remainder.
Ashmere Motors finances $27,650 at an illustrative 7.15 percent. At 36 months the installment is $855.65. At 60 months it is $549.46. At 72 months it is $473.40. At 84 months it is $419.34. Each step down is a smaller monthly load. Each step down is also more months of unpaid principal still sitting against the car.
The 36-month figure is $855.65 − $419.34 = $436.31 a month larger than the 84-month figure. That is the whole of the attraction of the longer term: the carrying cost printed on the glass falls. Track 1 lesson 3 is the securities version of the same direction. Drawing more of a line against an unchanged portfolio raises the claim on the asset while the asset sits still. Stretching a car term raises the claim that will eventually be paid, against a car that is not getting more valuable for the extra years.
The next lesson computes the totals. This one is only the month. Four rates, one principal, four remainders. The glass will show the smallest of them if the term is the longest of them.
A smaller installment is a longer clock. The formula does not have a way to shrink the month without adding months.
Key terms
- Term length
- The number of months n in the installment formula. Stretching it shrinks the payment.
- Periodic load
- The cash that leaves the account each month. Falls as n rises, holding P and r fixed.
- Outstanding claim
- The principal still sitting against the car. A longer term leaves more of it unpaid for longer.
Worked example
One principal, four remainders
Ashmere Motors. Principal $27,650, illustrative 7.15 percent APR. Term varies.
- 36 months
- $855.65
- 60 months
- $549.46
- 72 months
- $473.40
- 84 months
- $419.34
- 36-month minus 84-month installment
- $436.31
$27,650 × r × (1+r)^36 / ((1+r)^36 − 1), r = 0.0715 ÷ 12.
$855.65 − $419.34.
The glass can print $419.34 or $855.65 for the same $27,650. The difference is how many months the claim is allowed to sit.
Check yourself
Principal $21,200, illustrative 6.8 percent APR. What is the installment at 36 months, at 60 months, and at 84 months?
Stretching the term is the everyday version of shrinking the periodic load while raising the total claim on the asset, the same direction as drawing more of a line against an unchanged portfolio in Track 1 lesson 3. Open Advance rate versus market value →
Saved in this browser only. No account, nothing sent anywhere.
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.