Elliot Karlin is a​ 35-year-old bank executive who has justinherited a large sum of money. Having spent several years in the​bank's investments​ department, he's well aware of the concept ofduration and decides to apply it to his bond portfolio. In​particular, Elliot intends to use $ 1 million of his inheritance topurchase 4 U.S. Treasury​ bonds: 1. An 8.66 %​, ​13-year bond​that's priced at $ 1,096.15 to yield 7.49 %. 2. A 7.776 %​,​15-year bond​ that's priced at $ 1016.49 to yield 7.59 %. 3. A​20-year stripped Treasury​ (zero coupon)​ that's priced at $ 198.52to yield 8.25 %. 4. A​ 24-year, 7.41 % bond​ that's priced at $956.93 to yield 7.81 %. Note that these bonds are semiannualcompounding bonds. a. Find the duration and the modified durationof each bond. b. Find the duration of the whole bond portfolio ifElliot puts $ 250,000 into each of the 4 U.S. Treasury bonds. c.Find the duration of the portfolio if Elliot puts $ 370,000 eachinto bonds 1 and 3 and $ 130,000 each into bonds 2 and 4. d. Whichportfolio-b or c-should Elliot select if he thinks rates are aboutto head up and he wants to avoid as much price volatility as​possible? Explain. From which portfolio does he stand to make morein annual interest​ income? Which portfolio would you​ recommend,and​ why?