Krishna buys an n-year 1000 bond at par. The Macaulay duration is 7.959 years using an annual effective interest rate of 7.2%.

Calculate the estimated price of the bond, using the first-order modified approximation, if the interest rate rises to 8.0%.

• 940.60
• 942.88
• 944.56
• 947.03
• 948.47

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

[[math]] \begin{array}{l}{{\overline{{{v}}}=\frac{7.959}{1.072}=7.425}}\\ {{P(0.08)=P(0.072)\bigl[1-(\Delta i)\overline{{{v}}}\bigr]}}\\ {{P(0.08)=1000\bigl[1-(0.008)(7.425)\bigr]=940.60}}\end{array} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.