The formula for figuring the monthly payments on such a loan is
... A = P(r/12)/(1 -(1 +r/12)^(-12t))
where r is the annual interest rate (.065), P is the principal amount (we want to find), t is the number of years (30), and A is the monthly payment.
Filling in the given values, we have
... 821.69 = P(.065/12)/(1 - (1 +.065/12)^(-12*30)) = 0.00632068·P
Then the principal amount is
... P = 821.69/0.00632068 = 130,000.25
The most appropriate choice is ...
... 4. $130,000
