The following zero coupon bonds are currently trading in the market:

1-year zero coupon bond priced at $900

2-year zero coupon bond priced at $842

3-year zero coupon bond priced at $816

a) Based on these zero coupon bonds, calculate the 1 year, 2 year and 3 year spot rates. (Show your workings as a % to 2 decimal places e.g. 10.15%)

b) Is the yield curve for this bond upward sloping, downward sloping, or flat? Do a rough drawing of this yield curve using the three spot rates above. Label the axes, clearly show the slope (if any) of the yield curve, and indicate the three spot rates on the curve

c) You would like to purchase a 3-year coupon bond with a coupon of 7% (paid annually) and a face value of $1,000. What price would you expect to pay for this coupon bond? (Show your workings to 3 decimal places). Is the bond trading at a discount or premium? Explain briefly.

d) In an environment where interest rates are always positive, is it possible for a zero coupon bond to trade at a premium to face value? Explain briefly.