The monthly mortgage payment on your house is $821.69. it is a 30 year mortgage at 6.5% compounded monthly. how much did you borrow?

To find present value from monthly payments, we use
P_A=A((1+i)^n-1)/(i(1+i)^n)
where
A=monthly payment = $821.69
i=monthly interest rate = 6.5%/12 = 0.065/12
n=number of months = 30*12 = 360
Therefore
Present value
= amount borrowed
=A((1+i)^n-1)/(i(1+i)^n)
=821.69*((1+0.065/12)^360-1)/((0.065/12)*(1+0.065/12)^360)
= 130000.25
(note: the 0.25 could well be a round off error because the monthly payment is only accurate to the cent)

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