A second mortgage was taken for $150,000 for a term of 5 years @ 4.5% amortized over a period of 30 years. The current balance of the mortgage is $143,740.37. The balance to maturity is not given. If the mortgage is to be sold @ 4%, then what is the price of the mortgage? Any help would be great. Thank you.
There are several ways of approaching this problem. One entails using several TVM formulas to calculate the monthly payment, the number of months already paid, the balance at maturity, and calculating the PV @ the sale rate of 4%.
The easiest method, however, is to use an amortization schedule to find what we are after, that is IF you are allowed to use amortization tables. But, we can do the same thing using an online Financial Calculator, such as this fine calculator:
https://arachnoid.com/finance/
First, I shall use this amortization table to get most what we are after:
http://www.calculator.net/amortization-calculator.html?cloanamount=150000.00&cloanterm=30&cinterestrate=4.500&printit=0&x=58&y=26
From this table, we can readily get the monthly payment, the balance of the mortgage given in the question, number of months paid, the number of months remaining, and the balance of the mortgage after 5 years or 60 months. So, we have:
Monthly payment = $760.03
Current balance = $143,740.37
No. of months paid = 30
No. of remaining months = 30
Balance at maturity =$136,736.88
Now, will use the above financial calculator to calculate the sale price of the mortgage @ the given rate of 4% as follows:
Interest rate of 4% =4/12 =0.333333 under "ir"
No. of remaining months = 30 under "np"
The monthly payment = -760.03 under "pmt". Notice that we use "-" before 760.03 because it is "money owed"
Balance at maturity = -$136,736.88 under "fv". Notice that it is negative for the same reason as above.
Finally, we simply press the key labeled "pv", and it instantly gives us =$145,408.72, which is the price of this second mortgage at 4%.
