A ten-year certificate of deposit pays an annual effective interest rate of 8%. If the balance is withdrawn before the end of ten years, the purchaser can choose between two different penalties:

1. a loss of the last nine months’ interest.
2. a reduction in the annual effective rate of interest to j.

If the purchaser withdraws the funds after three years, the two penalties are equivalent.

Calculate j

• 5.74%
• 5.94%
• 6.14%
• 6.34%
• 6.54%

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

Solution: B

Assuming the loss of interest is the loss of the last 9 months interest:

[[math]] \begin{aligned} & (1.08)^{3-0.75}=(1.08)^{2.25}=1.189=(1+j)^3 \\ & j=5.94 \% \end{aligned} [[/math]]

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