You have to pay back a loan of $1,000 at the end of 6 years. You have to receive payments of $150, each from individual zero-coupon bonds investments, every 2 years beginning end of second year for the next 6 years (for a total of 3 payments). The market yield is assumed to be 4% on all the instruments and for all the maturities.

a. Calculate the present value of your assets PVA and liabilities PVL as described above. What is the present value of your surplus (PVA-PVL)?

b. Calculate the duration of your assets and liabilities.

c. Suppose there is an upward shift in the term structure and interest rates increase by 1%. Calculate the change in the value of your assets and liabilities. What is the net change in surplus value?