Elliot Karlin is a35-year-old bank executive who has just inherited a large sum of money. Having spent several years in thebank's investmentsdepartment, he's well aware of the concept of duration and decides to apply it to his bond portfolio. Inparticular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasurybonds:

1. An 8.56%, 13-year bondthat's priced at $1,087.93 to yield 7.49%.

2. A 7.847%, 15-year bondthat's priced at $1023.69 to yield 7.58%.

3. A20-year stripped Treasury(zero coupon)that's priced at $199.67 to yield 8.22%.

4. A24-year, 7.43% bondthat's priced at $954.93 to yield 7.85%.

Note that these bonds are semiannual compounding bonds.

a. Find the duration and the modified duration of each bond.

b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds.

c. Find the duration of the portfolio if Elliot puts $380,000 each into bonds 1 and 3 and $120,000 each into bonds 2 and 4.

d. Which portfoliob or cshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility aspossible? Explain. From which portfolio does he stand to make more in annual interestincome? Which portfolio would yourecommend, andwhy?