A 5-year $100,000 mortgage @ 5% compounded semi-annually with monthly payments amortized over 30 years was sold by the holder after 2 full years. If the holder wishes to get $100,000 for the remaining term, at what interest rate can he sell the mortgage? Any help will be great. Thanks.
A 5-year $100,000 mortgage @ 5% compounded semi-annually with monthly payments amortized over 30 years was sold by the holder after 2 full years. If the holder wishes to get $100,000 for the remaining term, at what interest rate can he sell the mortgage? Any help will be great. Thanks
1-We must convert 5% comp. S.A. to compounded monthly, which comes to=4.95%
2-We calculate the regular monthly payment for this mortgage, which comes to=$533.69
3-This formula is used the calculate the above payment:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $1
4-Through amortization, we will find the balance of the mortage at maturity, or 5 years from the day it was taken, which comes to=$91,761.78
5-Through iteration and interpolation, will find an interest rate that will equate th PV in 4 above plus the PV of the stream of payments in 2 above for the remaining 3 years, to equal $100,000 sale price.
6-The formulas used in 5 above are:
PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE.
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.
7-After a few attempts, we find that the interest rate required is=3.80771546545% comp.monthly, or about 3.87% effective annual equivalent.
