# How Loan Payments Vary by Down Payment

The amount you pay monthly or biweekly for a home or auto loan depends on four factors: the length of the lending term, the annual interest rate, the total price of the house or vehicle, and the down payment. The higher the down payment you make, the less you have to borrow, and thus the lower your periodic payments.

If you know the total cost and the loan conditions, you can compare different down payment options to see how they affect your monthly or biweekly payments. Apply the formulas below, or use the convenient down payment comparison calculator on the left.

### The Monthly (and Biweekly) Payment Equation

Given the amount borrowed*P*, the annual interest rate

*R*(decimal), and the number of years

*N*, the monthly payment

*M*is given by the formula

M =

(PR/12)(1 + R/12)

^{12N}/[(1 + R/12)

^{12N}- 1].

The biweekly payment *B* is given by the formula

B = (PR/26)(1 + R/26)^{26N}/[(1 + R/26)^{26N} - 1].

The number 12 appears in the first formula because there are 12 months in a year; the number 26 appears because there are 26 two-week periods in a year.

### How Periodic Payments Vary by Down Payment

If the total cost of the house or car is*C*and the down payment is

*D*, then

P = C - D.

For example, if a new vehicle costs $25,000 and you put $5,000 down, then you must borrow $20,000 and use P = 20000 in the formulas above.

You can also express

*D*as a percent of the total cost. If the down payment is

*X*% of the total cost, then the amount you must borrow is

P = C[1 - 0.01X]

For intance, suppose the price of a house is $230,000 and you must put 18% down. Then the amount you must borrow is

P = 230000[1 - 0.01(18)]

= 230000[1 - 0.18]

= 230000[0.82]

= 188600.

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