Amortization Formula

I wrote this Javascript calculator to enable the quick determination of monthly payments (x) for mortgages (also known as an amortization) based on the principal borrowed/amount of loan (P), the total number of payments (n), and monthly interest rate (r). The actual formula used can be seen in the image that accompanies this paragraph. This allows someone to quickly determine what effect different amounts borrowed and interest rates have on monthly payments.

Although I designed this for house mortgages, it works equally well for determining monthly payments to amortize car loans.

Note that the calculator automatically computes the values for n and r based on the values that you enter for number of years (y) and annual interest (i). It multiplies the number of years (y) times the number of months a payment must be made in a year (12) to come up with the total number of payments (n). It also divides the annual interest (i) by 12 (since mortgage interest is compounded monthly in the US) to come up with the monthly interest rate (r).

For example, consider a house that costs $250,000. Say you pay $50,000 up front and take out a mortgage for the remaining $200,000 (the P-value) at 6% annual interest (the i-value) for 30 years (the y-value). The calculator then determines the n and r-values and provides an output of $1,199.10 as the monthly payment to completely amortize the loan after 30 years.

Note that in Canada mortgage payments are made monthly, as in the US, but interest is compounded only bi-annually. This is better for the borrower because it results in less interest over the life of the loan. However, this calculator will not produce correct results for Canadian mortgages because it calculates an amortization schedule based on monthly compounding of interest.

The interest must be entered as a percentage and not a proportion. Put simply; 8% interest must be entered as 8 and not 0.08 (the calculator converts the percentage to a proportion for you).

Principal borrowed(P) - $:	# of payments (n = y*12):
Annual interest(i) - %:	Monthly interest (r = i/12):
Term in years(y):	Monthly payment (x):

Of course, this formula only works if you are actually paying some interest. The calculator accepts a value of 0 for interest (i) but uses the more simple formula of x = P / n to avoid a division by zero error (since r = i / 12 then r must equal zero if i equals zero).

Something worth keeping in mind when taking out a mortgage is that you will almost certainly have to pay property taxes and would be foolish to not pay for insurance. Those payments must be considered on top of the cost of the mortgage to determine if your budget can handle the mortgage.