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)