Lesson 13 of 25 · 6 min

Down payment on a house

Cash paid at the start sets day-one loan to value on a house that is still the same house.

A down payment, cash paid toward the price before the loan is written, sets day-one loan to value. Track 1 lesson 6 is that ratio: loan divided by collateral value. This lesson does not re-teach the ratio. It uses it on a house. The house does not change. P does. Every output of the installment formula scales with P.

LTV = loan ÷ asset

loan: The financed amount. Price minus down payment.
asset: The cash price of the house on day one.
LTV: The claim as a share of the house. Track 1 lesson 6's ratio.

Cairn Street Lending prices a house at $294,000. Five percent down is $14,700, financed $279,300, day-one LTV $279,300 ÷ $294,000 = 95.0 percent. Twenty percent down is $58,800, financed $235,200, LTV $235,200 ÷ $294,000 = 80.0 percent. At an illustrative 6.85 percent for 360 months, the 5 percent-down PI is $1,830.14. The 20 percent-down PI is $1,541.17.

The house is $294,000 both times. The 20 percent-down loan is $44,100 smaller, and the monthly PI is $1,830.14 − $1,541.17 = $288.97 smaller, because P fell, not because the rate or the house fell. Track 1 lesson 6 already showed that the same collateral produces two LTVs if the numerator changes. Cash at the start is that numerator change, done in dollars. The next lesson puts a charge on the 95 percent LTV. This one is only the ratio and the two installments.

A down payment does not cheapen the house. It shrinks the loan that sits on the house, which is the numerator Track 1 lesson 6 already named.

Key terms

Down payment: Cash paid toward the price before the loan is written. It reduces the principal.
Day-one LTV: Financed amount divided by cash price. On this book, 95.0 percent with 5 percent down, 80.0 percent with 20 percent down.
Financed amount: Cash price minus down payment. The P the installment formula uses.

Worked example

One house, two numerators

Cairn Street Lending. Price $294,000, illustrative 6.85 percent, 360 months.

5% down: $14,700
20% down: $58,800
Difference in P: $44,100
Difference in PI: $288.97

The house is $294,000 either way. Twenty percent down wrote an 80 percent LTV and a $1,541.17 installment because P was $235,200, not because the rate moved.

Check yourself

Price $228,000, illustrative 7.10 percent, 360 months. What is day-one LTV and PI with 5 percent down, and with 20 percent down?

A housing down payment sets day-one loan to value, the same ratio Track 1 lesson 6 computes. 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.