Lesson 6 of 25 · 6 min
How term length changes the total paid
The months you add back are extra accrual, so the cheaper installment is the more expensive loan.
The extra years are extra accrual. Lesson 5 showed the month shrinking as n rose. This lesson shows the total rising as those extra months keep charging interest on unpaid principal. The cheaper installment is the more expensive loan.
Same book as lesson 5: $27,650 at an illustrative 7.15 percent. At 36 months the total of payments is $30,803.38 and interest is $3,153.38. At 60 months the total is $32,967.72 and interest is $5,317.72. At 84 months the total is $35,224.81 and interest is $7,574.81. The 84-month loan costs $4,421.43 more in interest than the 36-month loan. That $4,421.43 is forty-eight extra months of a shrinking balance still accruing at 7.15 percent.
Track 1 lesson 14 is daily accrual on a securities line: interest is computed every day on that day's balance. A car loan is a coarser clock — monthly, not daily — but the same machine. Stretch the clock and the machine runs longer. The installment formula already contains this. Raising n lowers PMT and raises PMT × n. Both results come from one substitution.
The glass at Tallow Yard Autos will print the 84-month figure because it is the smaller month. The life of the loan prints the 84-month total because it is the larger claim. Those two printings are not in conflict. They are the two outputs of changing n.
A longer term does not add principal. It adds time, and time is what interest is charged on.
Key terms
- Total of payments
- The installment multiplied by the number of months. The whole cash claim of the loan.
- Extra interest
- The rise in life-of-loan interest when the same principal is spread over more months at the same rate.
- Interest clock
- The span of time unpaid principal is allowed to accrue. Lengthening it raises the total.
Worked example
The same $27,650, two clocks
Tallow Yard Autos. Principal $27,650, illustrative 7.15 percent APR. Compare 36 months with 84.
- 36-month total
- $30,803.38
- 60-month total
- $32,967.72
- 84-month total
- $35,224.81
- Extra interest, 36 versus 84
- $4,421.43
Interest $3,153.38.
Interest $5,317.72.
Interest $7,574.81.
$7,574.81 − $3,153.38.
Forty-eight extra months cost $4,421.43 of interest on an unchanged $27,650. The month got cheaper. The loan did not.
Check yourself
Principal $18,400, illustrative 8.1 percent APR. What is the payment and the total of payments at 36 months, and at 84 months?
The extra years are extra accrual, the everyday version of a longer interest clock — Track 1 lesson 14's daily accrual stretched across more months. Open Daily accrual, and why a monthly statement hides it →
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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.