50. The article titled Risk of Ultra-Low Yields includes the following information: Low yields mean that more and more of the value of a bond is in the big lump sum investors get when the bonds mature, making prices more volatile. This is because the payment of that lump sum may be many years away, making the bond's value sensitive to assumptions about interest rates. That has made long-maturity bonds, such as 10-year or longer paper, even riskier than in the past. For a one-percentage point rise in yields, 10-year U.S. Treasury holders now face a drop in price of nearly nine percentage points, versus around seven under more normal yield assumptions. Moreover, given where yields are, there is more room for them to rise than fall, meaning losses are more likely. The benchmark 10-year Treasury was yielding around 1.95% on Friday [when the article was written], only a sliver more than inflation, which is running at 1.7%. If yields were to return to more normal levels of around 4%, investors would see the price of the bond fall from 97.15 on Friday to around 81, a fall of more than 16%, a huge hit for an asset many see as super safe. If the 10-year Treasury, which pays interest semi-annually, had a yield to maturity of 1.95% and was priced at 97.15, the coupon rate on the bond would be:

51. Referring to the information from question 50, if the yield on the 10 year bond increases from 1.95% to 4% and the price of the bond falls from 97.15 to 81, then the modified duration of the 10 year Treasury would be:

1. 4.06 years
2. 4.16 years
3. 7.95 years
4. 8.11 years
5. 8.53 years