Lesson 1 of 25 · 6 min
Why a quote leads with the monthly number
The figure on the glass is a carrying cost, not a price, and the two answers are not interchangeable.
The number on the windscreen at Ashmere Motors is a carrying cost, the installment that services a loan, not a cash price, and the two figures answer different questions. A cash price is the amount that retires the car today. A carrying cost is the monthly amount that services a different principal over a chosen term at a chosen rate. Treating them as interchangeable is how a cheaper month becomes a larger claim.
Take a cash price of $31,460. A down payment of $2,500, cash paid before the first installment, leaves a financed amount of $31,460 − $2,500 = $28,960. At an illustrative 7.9 percent APR over 76 months the installment is $485.52. That $485.52 is the number on the glass. It is not $31,460, and it is not $28,960.
The exact installment, run across 76 months, produces a total of payments of $36,899.73. Subtract the $28,960 of principal and the interest over the life is $7,939.73. The monthly figure hid a claim of $36,899.73 against a car that cost $31,460 in cash. The extra $7,939.73 is time. It is not a feature of the car.
What the monthly number conceals, because it is a remainder rather than a price:
- The principal being financed, which is cash price minus down payment.
- The term over which that principal is spread.
- The rate at which unpaid principal accrues.
- The total of installments, which is the actual claim on the life of the loan.
A quote that leads with the month is stating a facility by its carrying cost. The price is a different line, and it is still the line that has to be paid, with interest, over the term.
Key terms
- Cash price
- The amount that buys the car today, before any loan is written.
- Carrying cost
- The monthly installment that services a financed principal at a stated rate and term.
- Financed amount
- Cash price minus the down payment. The principal the installment is computed on.
Worked example
The glass, the principal, and the life
Ashmere Motors quotes $485.52 a month on a car with a cash price of $31,460. Down payment $2,500. Term 76 months. Illustrative APR 7.9 percent.
- Financed amount
- $28,960
- Monthly rate r
- 0.00658333
- Installment
- $485.52
- Total of payments
- $36,899.73
- Interest over the life
- $7,939.73
$31,460 − $2,500.
7.9% ÷ 12, illustrative.
$28,960 × r × (1+r)^76 / ((1+r)^76 − 1).
Exact installment × 76.
$36,899.73 − $28,960.
The month is a carrying cost of $28,960. The cash price is $31,460. Those are not two ways of saying the same thing.
Check yourself
A car is financed at $21,980, illustrative 6.4 percent APR, 48 months. What is the monthly installment?
Leading with the monthly figure is the everyday version of stating a facility by its carrying cost rather than by its loan to value, the ratio Track 1 lesson 6 computes on a pledged portfolio. Open Loan to value, and how to compute 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.