Bruce deposits 100 into a bank account. His account is credited interest at an annual nominal rate of interest of 4% convertible semiannually. At the same time, Peter deposits 100 into a separate account. Peter’s account is credited interest at an annual force of interest of δ .After 7.25 years, the value of each account is the same.

Calculate δ .

• 0.0388
• 0.0392
• 0.0396
• 0.0404
• 0.0414

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

Solution: C

Given the same principal invested for the same period of time yields the same accumulated value, the two measures of interest [math]i^{(2)}=0.04[/math] and [math]\delta[/math] must be equivalent, which means:

[[math]] \begin{array}{l}{{\left(1+\frac{i^{(2)}}{2}\right)^{2}=e^{\delta},}}\\ {{e^{\delta}=\left(1+\frac{i^{(2)}}{2}\right)^{2}=1.02^{2}=1.0404}}\\ {{\delta=\ln(1.0404)=0.0396.}}\end{array} [[/math]]

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