The mortgage on your house is five years old It required monthly payments of $1,
ID: 2758236 • Letter: T
Question
The mortgage on your house is five years old It required monthly payments of $1,450, had an original term of 30 years, and had an interest rate of 10% (APR). In the intervening five years, interest rates have fallen and so you have decided to refinance-that is, you will roll the outstanding balance into a new mortgage The new mortgage has a 30-year term, requires monthly payments, and has an interest 6.625% (APR). What monthly repayments will be required with the new loan? If you still want to pay off the mortgage m 25 years, what monthly payment should you make after you refinance? Suppose you are willing to continue making monthly payments of $1,450, and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing? (Note Be careful not to round any Intermediate steps less than six decimal places) If you still want to pay off the mortgage in 25 years, the monthly repayments will be $ 1,089.93. (Round to the nearest cent) Suppose you are willing to continue making monthly payments of $1,450. How long will it take you to pay off the mortgage after refinancing? It will take approximately months Round to the nearest integer) Suppose you are willing to continue making monthly payments of $1,450 and want to pay off the mortgage m 25 year. How much additional cash can you borrow today as part of the refinancing?Explanation / Answer
To calculate the outstanding balance of original mortgage today, we first note that there are 25x12 months=300 months remaining on the loan. The monthly discount rate is 10%/12=0.8333%. So, the outstanding balance can be computed using the present value formula,
PV = [(1450/0.008333)(1-(1/1.008333300))]=$159,568.
The monthly rate of new loan = 5.625%/12 = 0.46875%
Time required to pay off the loan with the payment of $1,450:
[(1450/0.0046875)(1-(1/1.0046875n))]=$159,568
0.515844828 = (1-(1/1.0046875n))
(1/1.0046875n) = 0.484155172
1.0046875n = 2.065454
Taking Logs: n = log(2.065454)/log(1.0046875) = 155.1037
So, the mortgage will be paid off in 155.1037/12 = 12 Years and 11 months
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