Bank P offers a 3-year certificate of deposit that pays an annual effective interest rate of 4%. In addition, a bonus of 2% of the initial investment is paid at the end of the 3-year period. Bank Q offers a 3-year certificate of deposit without any bonus.

Calculate the annual effective interest rate that Bank Q would have to offer to produce the same annual yield as the certificate from Bank P.

• 4.3%
• 4.4%
• 4.5%
• 4.6%
• 4.7%

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

Solution: D

The value of 1 invested with bank P after three years is 1.04³ + 0.02 = 1.144864. The yield from Bank Q satisfies

[[math]] 1.144864=\left(1+i\right)^{3}\Longrightarrow i=1.144864^{1/3}-1=0.04613=4.6\% [[/math]]

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