Sandra Kapple presents Maria VanHusen with a description, given in the following exhibit, of the bond portfolio held by the Star Hospital Pension Plan. All securities in the bond portfolio are non-callable U.S. Treasury securities.
Star Hospital Pension Plan Bond Portfolio

a. Calculate the effective duration of each of the following:
i. The 4.75% Treasury security due 2040
ii. The total bond portfolio
b. VanHusen remarks to Kapple, "If you changed the maturity structure of the bond portfolio to result in a portfolio duration of 5.25, the price sensitivity of that portfolio would be identical to the price sensitivity of a single, non-callable Treasury security that has a duration of 5.25." In what circumstance would VanHusen's remark be correct?

Price If Ylelds Change Down 100 Basls Polnts Current Price Up 100 Basis Effective Duration Par Value (U.S. $) Market Value Treasury Security 2.375% due 2015 4.75% due 2040 Total bond portfolio (U.S. $) Polnts $101.391 $48,667,680 103.595 2.15 9.245 $48,000,000 50,000,000 116.887 100.000 86.372 50,000,000 98,667,680 98,000,000