Jeff deposits 10 into a fund today and 20 fifteen years later. Interest for the first 10 years is credited at a nominal discount rate of d compounded quarterly, and thereafter at a nominal interest rate of 6% compounded semiannually. The accumulated balance in the fund at the end of 30 years is 100.

Calculate d.

• 4.33%
• 4.43%
• 4.53%
• 4.63%
• 4.73%

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

Solution: C

Equation of value at end of 30 years:

[[math]] \begin{array}{l}{{10(1-d/4)^{\frac{v0}{4}}(1.03)^{\frac{v0}{40}}+20(1.03)^{30}=100}}\\ {{10(1-d/4)^{-40}=[100-20(1.03)^{30}]/1.03^{40}=15.7738}}\\ {{d=4(1-0.98867)=0.0453 = 4.53\%.}} \end{array} [[/math]]

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