Berkshire Hathaway is contemplating the issue of a very unusual bond. Known as a “Bizarro Bond,” the security will provide an annual coupon payment of $50. The yield to maturity on the bond is 4 percent and the maturity value of the bond is the standard $1,000. However, the maturity date will fluctuate with inversely with the length of time that the coupons are paid. If the coupons are paid for N years, the bond will mature in (100-N) years.
Required: Compute the Macaulay duration of this bond for all integer values of N between zero and 100. Provide a detailed explanation of the computation when the value of N is equal to 15