For a 30-year fixed-rate mortgage with balance of $100,000 and mortgage rate of 6.00%, please do solve the followings: a. Assuming the borrower will pay the mortgage based on the schedule for next 30 years, i. What is the Average Life of the mortgage (in years)? ii. What is the PV of the mortgage if market mortgage rate goes up to 6.50%? iii. What is the PV of the mortgage if market mortgage rate goes up to 5.50%? iv. What is the effective duration according to the formular in slide 53? b. Assuming the borrower will pay the mortgage based on the schedule for first five years and pay off the mortgage at the end of fifth year, i. What is the Average Life of the mortgage (in years)? ii. What is the PV of the mortgage if market mortgage rate goes up to 6.50%? iii. What is the PV of the mortgage if market mortgage rate goes up to 5.50%? iv. What is the effective duration according to the formular in slide 53? formula in slide 53:

Deffective=2iPPupPdown Where, P is the current or base price of the bond, i is the yield curve or rate shock size for each size, Pup and Pdown are estimated up and down rate shocked prices with the constant OAS solved