Lesson 4 of 25 · 7 min
Total interest over the life, computed
Life-of-loan interest is a cost that lives in time, not a change in how much principal the car will support.
Total interest over the life is a cost that lives in time. It is not a change in how much principal the car will support. Capacity is a later comparison, loan against mark. Interest is what accrues on the outstanding balance while that comparison is running.
Marlow Street Garage finances $33,140 at an illustrative 7.9 percent for 76 months. The installment is $555.60. The total of payments is $42,225.72. Interest over the life is $42,225.72 − $33,140 = $9,085.72, which is $9,085.72 ÷ $33,140 = 27.42 percent of the principal. That 27.42 percent is not the APR. It is the APR, applied to a shrinking balance, summed across 76 months, expressed as a share of the starting principal.
The first month shows where the $9,085.72 begins. Interest on $33,140 at 7.9 percent is $33,140 × 0.079 ÷ 12 = $218.17. The installment is $555.60, so principal retired is $555.60 − $218.17 = $337.43. Most of the first payment is still principal at this rate and term, but $218.17 of it is time already used. Over 76 months those time slices add to $9,085.72.
Track 5 lesson 12 is the securities-backed version of the split: a rate is a cost in time, a capacity is a claim against an asset. Raising the rate on a car loan raises the $9,085.72. It does not, by itself, change how much of the car's mark the loan represents. Those are two different machines, and this lesson is the time machine only.
Interest as a share of principal is a life-of-loan fact. APR is a yearly restatement. They rhyme. They are not equal.
Key terms
- Interest over the life
- Total of payments minus principal. The whole time-cost of the loan, in dollars.
- Interest as a share of principal
- Life-of-loan interest divided by the starting principal. A different number from APR.
- First-month split
- The opening installment divided into interest on the starting balance and principal retired.
Worked example
Seventy-six months of time, in one subtraction
Marlow Street Garage. Principal $33,140, illustrative 7.9 percent APR, 76 months.
- Installment
- $555.60
- Total of payments
- $42,225.72
- Interest over the life
- $9,085.72
- As a share of principal
- 27.42%
- First-month interest
- $218.17
- First-month principal
- $337.43
$33,140 × r × (1+r)^76 / ((1+r)^76 − 1), r = 0.079 ÷ 12.
$42,225.72 − $33,140.
$9,085.72 ÷ $33,140.
$33,140 × 0.079 ÷ 12.
$555.60 − $218.17.
The loan's time-cost is $9,085.72. The car's capacity to support principal is a different question, and the first month has not answered it.
Check yourself
Principal $15,400, illustrative 6.9 percent APR, 60 months. What is the installment, the interest over the life, and the first-month split?
Life-of-loan interest is the everyday version of a cost that lives in time rather than in a capacity change, the split Track 5 lesson 12 draws between a rate and a capacity. Open A rate change is not a capacity change →
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.