Computing the issue price of bonds. Compute the issue price of each of the following bonds.

a. \(\$ 1,000,000\)-face value, zero coupon bonds due in 20 years, priced on the market to yield 12 percent compounded semiannually.

b. \(\$ 1,000,000\)-face value, serial bonds repayable in equal semiannual installments of \(\$ 50,000\) for 20 years, priced on the market to yield 6 percent.

c. \(\$ 1,000,000\)-face value, 10 -percent semiannual coupon bonds, with interest payable each six months and the principal due in 20 years, priced on the market to yield 8 percent.

d. \(\$ 1,000,000\)-face value semiannual coupon bonds, with an annual coupon rate of 6 percent for the first ten years and 14 percent for the second ten years and the principal due in 20 years, priced on the market to yield 10 percent.