Question

A house that was bought 8 years ago for $150,000 is now worth $300,000. Originally,the house was purchased by paying 20% down with the rest financed through a 25-year mortage at 10.5%. The owner (after making 96 equal monthly payments) is in need of cash, and would like to refinance the house. The finance company is willing to loan 80% of the new value of the house amortized over 25 years with the same interest rate. How much cash will the owner recieve after paying the balance of the original loan?

Answer 1

Solution: Original loan amount= 150,000 − (.20)150,000 = 120,000

Original monthly payments= V x i /1 − (1 + i)⁻ⁿ = 120,000 x .00875 /[1 − (1 + .00875)⁻³⁰⁰ ] = 1133.02 After making 96 payments the owner still owes 204 payments on the loan or

V = P x [1 − (1 + i) ⁻ⁿ ] / i = 1133.02 x [1 − (1 + .00875)⁻²⁰⁴ ] / .00875 = 107,590.94

If the house is refinanced for 80% of $300,000 or (.80)300,000=240,000. After paying off the first loan, the owner will have $240,000-$107,590.94=$132,409.06