a. To find the price of the bond when it was issued, we can use the present value formula for a bond:
Price = (C / r) x [1 - 1 / (1 + r)^n] + F / (1 + r)^n
where:
C = coupon payment = 0.07 x $1,000 = $70 per year
r = yield to maturity = 0.06
n = number of years to maturity = 10
F = face value = $1,000
Plugging in the values, we get:
Price = ($70 / 0.06) x [1 - 1 / (1 + 0.06)^10] + $1,000 / (1 + 0.06)^10
Price = $828.47
Therefore, the price of the bond when it was issued was $828.47.
b. Immediately before the first coupon payment, the bond has accrued interest equal to the coupon payment. The price of the bond can be calculated using the present value of the remaining coupon payments and the face value:
Price = (C / r) x [1 - 1 / (1 + r)^n] + (C + F) / (1 + r)^n
where:
C = coupon payment = $70
r = yield to maturity = 0.06
n = number of years remaining until maturity = 10
F = face value = $1,000
Plugging in the values, we get:
Price = ($70 / 0.06) x [1 - 1 / (1 + 0.06)^10] + ($70 + $1,000) / (1 + 0.06)^10
Price = $875.14
Therefore, the price of the bond immediately before the first coupon payment is $875.14.
c. After the first coupon payment, there are 9 years remaining until maturity. The price of the bond can be calculated using the same formula as in part (b), but with one less year:
Price = (C / r) x [1 - 1 / (1 + r)^(n-1)] + (C + F) / (1 + r)^(n-1)
where:
C = coupon payment = $70
r = yield to maturity = 0.06
n = number of years remaining until maturity = 9
F = face value = $1,000
Plugging in the values, we get:
Price = ($70 / 0.06) x [1 - 1 / (1 + 0.06)^9] + ($70 + $1,000) / (1 + 0.06)^9
Price = $896.29
Therefore, the price of the bond immediately after the first coupon payment is $896.29.