Answer:
a.
Bond Price = $563,333.90007 rounded off to $563,333.90
b.
Bond Price = $502500
c.
Bond Price = $437232.16025 rounded off to $437232.16
Explanation:
To calculate the quote/price of the bond today, which is the present value of the bond, we will use the formula for the price of the bond. As the bond is a semi annual bond, we will use the semi annual coupon payment, semi annual number of periods and semi annual YTM. The formula to calculate the price of the bonds today is attached.
a. Case A: Market interest rate (annual): 4 percent
Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075
Total periods remaining (n) = 7 * 2 = 14
r or YTM = 4% * 6/12 = 0.02 or 2%
Bond Price = 15075 * [( 1 - (1+0.02)^-14) / 0.02] + 502500 / (1+0.02)^14
Bond Price = $563,333.90007 rounded off to $563,333.90
b. Case B: Market interest rate (annual): 6 percent
Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075
Total periods remaining (n) = 7 * 2 = 14
r or YTM = 6% * 6/12 = 0.03 or 3%
Bond Price = 15075 * [( 1 - (1+0.03)^-14) / 0.03] + 502500 / (1+0.03)^14
Bond Price = $502500
c. Case C: Market interest rate (annual): 8.5 percent.
Coupon Payment (C) = 502500 * 0.06 * 6/12 = $15075
Total periods remaining (n) = 7 * 2 = 14
r or YTM = 8.5% * 6/12 = 0.0425 or 4.25%
Bond Price = 15075 * [( 1 - (1+0.0425)^-14) / 0.0425] + 502500/(1+0.0425)^14
Bond Price = $437232.16025 rounded off to $437232.16
