A pension fund has liabilities to pay pensions each year for the next 60 years. The pensions paid will be $100m at the end of the first year, increasing by 0.04 each year. The fund holds government bonds to meet its pension liabilities. The bond matures at par in 35 years time and pay an annual coupon of 0.04. The effective annual rate of interest is 0.03.

a) The present value of the pension funds liabilities is: ____

b) The face amount of the bond that the fund need to hold so that the present value of the assents is equal to the present value of the liabilities is: ____

c) The duration of the assets is: ___

d) If there was a reduction in the rate of interest to 0.015 per annum effective, the value of the assets would change by: ____