P11.24 Elliot is a 35-year-old bank executive who has just inherited a large sum of money.

Having spent several years in the bank’s investments department, he’s well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use

$1 million of his inheritance to purchase three bonds:

a. An 8.5%, 13-year bond that’s priced at $1045 to yield 7.47%

b. A 7.875%, 15-year bond that’s priced at $1020 to yield 7.60%

c. A 24-year, 7.5% bond that’s priced at $955 to yield 7.90%

Find the duration and the modified duration of each bond.