1. Calculate the duration of a $100,000 fixed-rate 30-year mortgage with a nominal annual rate of 7.0%. What is the expected percentage change in value if the required rate drops to 6.5% immediately after the mortgage is issued?
2. The value of a $100,000 fixed-rate 30-year mortgage falls to $89,537 when interest rates move from 5% to 6%. What is the approximate duration of the mortgage?
3. Calculate the duration of a commercial loan. The face value of the loan is $2,000,000. It requires simple interest yearly, with an APR of 8%. The loan is due in four years. The current market rate for such loans is 8%.