# How Much Should I Put Down?

How Much Down?
Total Cost
Number of Years
Annual Interest Rate (decimal)
Monthly or Biweekly?
Desired Periodic Payment

How much to put down on a new house or car depends on how much the item costs, how much you want to pay each month (or every two weeks), the annual interest rate, and the number of years in the lending term.

You can use the periodic payment formula to determine the right down payment, or use the convenient calculator on the left.

To use the down payment calculator, input the total cost of the home or vehicle, the number of years, the interest rate as a decimal, the type of periodic payment (monthly or biweekly), and the desired payment each period.

### The Down Payment Equation

If the total cost of the item is C and the down payment D, then the monthly and biweekly payments M and B are given by the equations

M = (C-D)(R/12)(1 + R/12)12N/[(1 + R/12)12N - 1] and
B = (C-D)(R/26)(1 + R/26)26N/[(1 + R/26)26N - 1],

where R is the interest rate expressed as a decimal and N is the number of years. You can solve each of these equations for D:

D = C - (12M/R)[(1 + R/12)12N - 1]/(1 + R/12)12N    monthly
D = C - (26B/R)[(1 + R/26)26N - 1]/(1 + R/26)26N    biweekly

### Example

Suppose a new home costs \$205,000, the annual interest rate is 6.3%, the number of years in the lending period is 20, and you can make monthly payments of \$945. To figure your down payment, first assign values to the four variables:

C = 205000
M = 945
N = 20
R = 0.063

Now plug these into the first down payment formula:
D = 205000 - (12*735/0.063)[1.00525240 - 1]/1.00525240
= 205000 - 180000(2.513821)/(3.513821)
= 205000 - 128773.71
= 76226.29

So you must put \$76,226.29 down in order to afford these loan terms. If you can't afford that down payment, you will either need to make larger monthly payments, increase the length of the lending term, or secure a lower interest rate.