Revision as of 21:56, 17 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>4.33%</li><li>4.43%</li><li>4.53%</li><li>4.63%</li><li>4.73%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
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.
ABy Admin
Nov 17'23
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.