Eric puts in a deposit where the bank credits him a rate of discount of 13% convertible every 4 years. Billy wants to find the same rate or better, but can only find banks that will give him rates of interest convertible monthly. What is the lowest rate of interest Billy will accept?

• .182
• .185
• .034
• .105
• .2014

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: B

Rate of discount: 13% convertible every 4 years

Find the equal rate of interest convertible monthly:

[[math]] \begin{gathered}(1-\mathrm{d} / \mathrm{n})^{-\mathrm{n}}=(1+\mathrm{i} / \mathrm{n}) \\ (1-.13 /(1 / 4))^{-1 / 4}=(1+\mathrm{i} / 12)^{12} \\ 1.2014=(1+\mathrm{i} / 12)^{12} \\ .185=\mathrm{i}\end{gathered} [[/math]]

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.