posted by scotty .
You have just purchased a house and have obtained a 30-year, $200,000 mortgage with an interest rate of 10 percent.
a. what is your annual payment?
b. Assuming you bought the house on Jan. 1st, what is the principle balance after one year?
c. After four years, mortgage rates drop to 8 percent for 30-year fixed-rate mortgages. You still have the old 10 percent mortgage you signed four years ago and you plan to live in the house for another five years. The total cost to refinance the mortgage is $3,000 including legal fees, closing costs and points. The rate o a five-year CD is 6 percent. Should you refinance your mortgage or invest the $3,000 in a CD? The 6 percent CD rate is your opportunity cost of capital.
a. The present value of a mortgage equals the period payment times the annuity factor?
a. Pt = (Po*r*t)/(1-(1+r)^-t.
Po = $200,000.
r = (10% / 12)/100% = 0.0083333 = Monthly % rate expressed as a decimal.
t = 30yrs * 12mo/yr = 360 Months.
Plug the above values into the given Eq
Pt = $631,850.40.
Monthly(I+P) = Pt/t = $1755.14.
Annual = 1755.14/mo * 12mo = $21,061.68.
b. Bal. = 631,850.40 - 21,061.68 =