Lesson 7 of 25 · 6 min

What a down payment does to the financed amount

Cash paid before the first installment is a smaller principal, which is a smaller claim against the same car.

A down payment, cash paid toward the price before the loan is written, lowers the principal. The car does not change. The rate and the term need not change. What changes is P in the installment formula, and every output of that formula scales with P.

Cinderwell Dealer prices a car at $33,890, at an illustrative 7.4 percent for 60 months. With $0 down the financed amount is $33,890, the installment is $677.48, and interest over the life is $6,758.61. With $2,500 down the financed amount is $31,390 and the installment is $627.50. With $5,000 down the financed amount is $28,890, the installment is $577.52, and interest over the life is $5,761.47.

The $5,000 down payment cuts the principal by $5,000 and cuts life-of-loan interest by $6,758.61 − $5,761.47 = $997.14. The installment falls by $677.48 − $577.52 = $99.96 a month. Over the life the two totals differ by $5,997.14 — the $5,000 of principal plus the $997.14 of interest that principal would have accrued. Track 1 lesson 4 is the same direction on a pledged portfolio: a haircut, the percentage of market value the lender withholds, lowers the loan relative to the asset. Cash paid at the start is that lowering, done in dollars rather than in a percentage.

The next lesson puts the same $5,000 against the car's mark as a ratio. This one is only the principal. Smaller P, smaller installment, smaller interest, same car.

A down payment does not cheapen the car. It shrinks the loan that sits on the car.

Key terms

Down payment: Cash paid toward the price before the loan is written. It reduces the principal.
Financed amount: Cash price minus down payment. The P the installment formula uses.
Haircut (everyday form): A lowering of the loan relative to the asset. On a car, cash at the start does in dollars what Track 1 lesson 4 does in a percentage.

Worked example

Three down payments, one car

Cinderwell Dealer. Cash price $33,890, illustrative 7.4 percent APR, 60 months.

$0 down, financed: $33,890
$2,500 down, financed: $31,390
$5,000 down, financed: $28,890
Interest saved by $5,000 down: $997.14

Five thousand dollars of cash at the start removed $5,000 of principal and $997.14 of the interest that principal would have carried. The car is still $33,890.

Check yourself

Cash price $29,840, illustrative 6.6 percent APR, 60 months. What is the installment with $0 down, and with $3,000 down?

A down payment is the everyday version of a haircut: it lowers the loan relative to the asset, the same direction Track 1 lesson 4 explains. Open What a haircut is, and why it exists →

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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.