Question

A $275,000 face value Province of British Columbia bond carrying a 10.6% coupon is issued on September 5, 1990, with 30 years until maturity. The bond is purchased on March 5, 2002, when posted rates are 5.98%. Calculate the purchase price of the bond. What is the amount of its premium or discount?

Answer 1

To calculate the purchase price of the bond, use the present value formula. The discount rate is 5.98% and the coupon payment is $29,150 per year. Subtract the purchase price from the face value to find the amount of premium or discount.

Step-by-step explanation:

To calculate the purchase price of the bond, we can use the present value formula. The coupon payment is calculated as $275,000 x 10.6% = $29,150 per year. The discount rate, which is the posted rate of 5.98%, is used to calculate the present value of the coupon payments. The present value of the coupon payments is then added to the present value of the face value to get the purchase price of the bond.

The discount rate is 5.98% so the present value of the coupon payment is:

($29,150 / (1 + 5.98%)^12) + ($29,150 / (1 + 5.98%)^11) + ... + ($29,150 / (1 + 5.98%)^1)

The present value of the face value is:

$275,000 / (1 + 5.98%)^12

The purchase price of the bond is then the sum of the present value of the coupon payments and the present value of the face value.

To calculate the amount of premium or discount, subtract the purchase price from the face value of the bond.