A second mortgage of $125,000 was taken on a property for a period of 5 years amortized over a 30-year period and carrying an interest rate of 5.45% compounded annually. It has a current balance of $120,949.33 and is to be sold in the secondary market at the rate of 6.5% compounded monthly. What is the selling price of this mortgage? Thanks for help.
1) This is quite involved and would be difficult for most students to solve correctly.
Notice that it doesn't give the monthly payment, so it must be calculated first. Also, notice that the interest rate is 5.45% comp. annually, which has to be converted to comp.monthly to match the payments. So, 5.45% comp annually =5.32% comp. monthly.
2) So now we can calculate the monthly payment on $125,000 over 30 years, or 360 months @ 5.32% and we we get =$695.68. We know that the balance of the mortgage is $120,949.33, but it doesn't say how many payments remain to be paid until the mortgage matures in 5 years or 60 months. But we can easily figure out the balance of the mortgage after 5 years or 60 months, which comes to=$115,296.96. Between this balance and the balance given, or $120,949.33, we can easily figure out the number of payments made and the number of payment remaining in the 5-year period, which is important. It turns out that 27 payments have already been made and 33 more payments remain to be paid till maturity.
3) Since now we have the balance of the mortgage after 5 years, or $115,296.96, and 33 payments of $695.68 each remain to be paid, we can easily figure out their PV @ the market rate given, namely 6.50% comp. monthly. Combining the two PV's for the remaining 33 months @ 6.50% we get a total of =$117,441.99, which is the selling price of this second mortgage.
4) I have skipped all the common TVM fomulas used here for the sake of brevity, since they are labour-intensive and time consuming. To solve this problem in detail would take perhaps 2-3 full pages to arrive at the final solution. I have double-checked it and it appears to give the same consist result calculated in 3) above.
5) If you have any questions, or don't understand something, just let us know here. Good luck to you.
