Question

Eight years ago you borrowed $142,000 at a fixed annual rate of 10.5 percent p.a. to buy a house. Your loan is a 30-year, monthly payment loan. Calculate the current payoff of the loan (immediately after the 112th payment) assuming that you did not make any additional payments for the first 112 payments

Answer 1

Answer:

   $Payoff=\ 131,338.81$

Explanation:

Except for other fees or interests that you might owe, the payoff should be equal to the debt balance. Then, assuming no other fees or interests that you might owe, you just must calculate the balance of your debt after 112 payments (11 years, not 8).

There is a very important formula to calculate the outsdanging balance of a loan, whithout calculating the complete sheet of all the monthly payments:

       $balance=Loan\times \dfrac{[(1+r)^n-(1 + r)^m]}{[(1+r)^n-1]}$

Where:

• balance is the outstanding balance after m months

• r i s the fixed monthly rate: 10.5%/12 = 0.105/12

• n is the number of total months of the loan: 30years × 12month/year = 360 months

• m: 112

       $balance=\ 142,000\times \dfrac{[(1+(0.105/12))^{112}-(1 + (0.105/12))^{112}]}{[(1+(0.105/12))^{360}-1]}$

      $balance=\ 131,338.81$