A 5-year term mortgage, amortized over 30-year period, was taken on a property for $250,000 @ 5% compounded semi-annually. After 30 monthly payments were made on time, it was sold to yield 4% compounded semi-annually. What was the sale price of the mortgage? Thanks for any help.
This is an uncommon and rather involved calculation:
1) Convert the two interest rates, 4% and 5% from semi-annual comp. to monthly comp.
4% = 3.96706838956 and 5% =4.94869855817.
2) Calculate the monthly payment of the mortgage amortized over 30 years. And that comes to:
= $1,334.23.
3) Find the balance of the mortgage at the end of 5 years, which comes to=$229,404.06
4) Find the PV of the anove balance in 3 PLUS the PV of the remaining 30 payments of $1,334.23 each at the sale price of 4%.
5) The totals in 4 above come to: $207,778.33 + $38,046.27 =$245,824.60, which is the sale price of this mortgage @ 4% comp. semi- annually.
