. A mortgage company issues a 100,000 two-year mortgage which carries an effective annual interest rate of 5%. The mortgage is repaid by two equal payments at the end of each year. The borrower may repay the mortgage at the end of the first year without penalty. With equal probablity the interest rate at the end of the first year will go up 1%, stay the same, or go down 1%. The mortgage company can reinvest all proceeds at the new interest rate. Independently of the interest rate, the borrower has a 3% probability of defaulting at the end of the first year and a 2% probability of defaulting at the end of the second year. Assume that the borrower uses the prepayment option if it is advantagous and doesnt default.

A mortgage company issues a 100,000 two-year mortgage which carries an effective annual interest rate of 5%. The mortgage is repaid by two equal payments at the end of each year. The borrower may repay the mortgage at the end of the first year without penalty. With equal probablity the interest rate at the end of the first year will go up 1%, stay the same, or go down 1%. The mortgage company can reinvest all proceeds at the new interest rate. Independently of the interest rate, the borrower has a 3% probability of defaulting at the end of the first year and a 2% probability of defaulting at the end of the second year. Assume that the borrower uses the prepayment option if it is advantagous and doesn't default. (a) Find the expected accumulated value of this mortgage to the mortgage company at the end of two years. (b) Find the standard deviation of the accumulated value of this mortgage to the mortgage company at the end of two years. (c) Find the expected yield rate of this mortgage to the mortgage company at the end of two years. (d) Find the standard deviation of the yield rate of this mortgage to the mortgage company at the end of two years. A mortgage company issues a 100,000 two-year mortgage which carries an effective annual interest rate of 5%. The mortgage is repaid by two equal payments at the end of each year. The borrower may repay the mortgage at the end of the first year without penalty. With equal probablity the interest rate at the end of the first year will go up 1%, stay the same, or go down 1%. The mortgage company can reinvest all proceeds at the new interest rate. Independently of the interest rate, the borrower has a 3% probability of defaulting at the end of the first year and a 2% probability of defaulting at the end of the second year. Assume that the borrower uses the prepayment option if it is advantagous and doesn't default. (a) Find the expected accumulated value of this mortgage to the mortgage company at the end of two years. (b) Find the standard deviation of the accumulated value of this mortgage to the mortgage company at the end of two years. (c) Find the expected yield rate of this mortgage to the mortgage company at the end of two years. (d) Find the standard deviation of the yield rate of this mortgage to the mortgage company at the end of two years