Question

The mortgage on your house in Winnipeg is five years old. It required monthly payments of $1402, had an original term of 30 years, and had an interest rate of 9% (APR with semiannual compounding). In the intervening five years, interest rates have fallen, housing prices in the United States have fallen, and you have decided to retire to Florida. You have decided to sell your house in Winnipeg and use your equity for the down payment on a condo in Florida. You will roll over the outstanding balance on your old mortgage into a new mortgage in Florida. The new mortgage has a 30-year term, requires monthly payments, and has an interest rate of 6.625% (APR with monthly compounding, which is typical for U.S. mortgages).

**please list out step by step actions, please show the formulas used, please DONT USE excel**

Answer 1

Step 1: Find the monthly compounded rate
rate compounded monthly=((1+r/2)^(2/12)-1)*12=((1+9%/2)^(2/12)-1)*12=8.836%

Step 2: Find the original loan amount
Loan amount=Monthly payments/(r/12)*(1-1/(1+r/12)^(12*n))=1402/(8.836%/12)*(1-1/(1+8.836%/12)^(12*30))=176830.2836

Step 3: Find loan balance now
Loan remaining=Loan*(1+r/12)^(12*t)-Monthly payments/(r/12)*((1+r/12)^(12*t)-1)=176830.2836*(1+8.836%/12)^(12*5)-1402/(8.836%/12)*((1+8.836%/12)^(12*5)-1)=169324.7793

1.
What monthly repayments will be required with the new loan?
Find new monthly payments
Monthly payments=Loan*(rate/12)/(1-1/(1+rate/12)^(12*n))=169324.7793*(6.625%/12)/(1-1/(1+6.625%/12)^(12*30))=1084.2051

2.
If you still want to pay off the mortgage in 25 years, what monthly payment should you make on your new mortgage?
Monthly payments=Loan*(rate/12)/(1-1/(1+rate/12)^(12*n))=169324.7793*(6.625%/12)/(1-1/(1+6.625%/12)^(12*25))=1156.5538