Alex earned an investment income of $13,000 during 1999. The beginning and ending balances were $114,000 and $136,000. A deposit was made at time k during the year. No other deposits or withdrawals were made. The fund made 11% in 1999 using the dollar-weighted method.

Determine k.

• August 1
• May 1
• June 1
• July 1
• March 1

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

Solution: D

Beginning= 114,000 End=136,000

Investment Income= 13,000 i= .11

Total Increase =22,000

Deposit= Total Income- Investment Income= 9,000

Dollar-Weighted:

[[math]] \begin{aligned} 114,000(1.11) + 9000(1+.11(1-k))= 136,000 \\ -10,000*.11k=-530 \\ k= .4818≈.5 \\ \end{aligned} [[/math]]

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