Question 231050
On December 31, 1995, a house is purchased with the buyer taking out a 30-year $90,000  mortgage at 9% interest compounded monthly. The mortgage payments are made at the end of each month.  Calculate the amount of the monthly payment.


Assuming he starts paying in January, the answer should be:


$724.1603553


Let's see how we did.


PAYMENT FOR A PRESENT VALUE
{{{ PMT(PV) = (PV / ((((1 - (1 / ((1+i)^n))))/i))) }}}
PMT = Payment per Time Period	
PV = Present Value
i = Interest Rate per Time Period
n = Number of Time Periods


We set the variables as follows:


PMT is what we want to find.
PV = $90,000 which is the cost of the mortgage.
i = 9% / 100% / 12 = .09/12 = .0075 per time period.
n = 30 years * 12 = 360 time periods.


We plug these values into the formula to get:


{{{ PMT(PV) = (90000 / ((((1 - (1 / ((1.0075)^360))))/.0075))) }}}


Since this equals 724.1603552, the answer we expected is confirmed.


I did it using a financial calculator first and then followed up with the equation.  The equation assumes end of time period payments.


Looks like that's your answer.