Final answer:
The price paid for a 50-year Government of Canada bond on December 31st, 2006 with a coupon rate of 6.20% and a yield to maturity of 7.40% would have been less than its face value of $10,000,000, calculated by discounting the future coupon payments and the face value at the yield to maturity rate.
Step-by-step explanation:
When calculating the price of a 50-year Government of Canada bond with a face value of $10,000,000, a coupon rate of 6.20%, and quarterly coupon payments on December 31st, 2006, one must consider the yield to maturity on that date which was 7.40% when the term structure of interest rates was flat. Since coupon payments are quarterly, the annual coupon payment is divided by four to get the quarterly payment amount, which will be 6.20% of $10,000,000, resulting in $620,000 annually or $155,000 quarterly.To find out how much one would pay for the bond, you need to calculate the present value of all future coupon payments along with the present value of the face value of the bond. You would discount these amounts using the yield to maturity as the discount rate. As interest rates were higher at the time of purchase (7.40%) than the coupon rate (6.20%), the bond would have been purchased at a discount, meaning for less than its face value.
The present value of the bond is calculated using the formula Present Value = (C / r) * (1 - (1 + r)-n) + F / (1 + r)n, where C is the annual coupon payment, r is the yield to maturity (expressed as a decimal), n is the total number of periods, and F is the face value of the bond. However, given that this is a simplified summary and the actual calculations for bonds with many periods can be quite complex and lengthy, and require either a financial calculator or spreadsheet software, we will forgo the actual calculation in this explanation.