On February 1, Sawyer’s investment is worth $900. On August 1, the value has increased to $1600 and Sawyer deposits $D. On December 1, the value is $1400 and $400 is withdrawn. On February 1 of the following year, the investment account is worth $800. The time-weighted interest is 3%.

Calculate the dollar-weighted rate of interest.

• Insufficient information given to complete problem
• -.685
• -.033
• -.045
• -.142

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

Solution: C

Feb 1	Aug 1	Dec 1	Feb 1
900	1600	1400	800
	1600 + D	1000

Time Weighted Rate of interest:

[[math]] \begin{aligned} & {[1600 / 900] *[1400 /(1600+\mathrm{D})] *[800 / 1000]-1=.03} \\ & \quad \Rightarrow D=333.12 \end{aligned} [[/math]]

Dollar-Weighted:

[[math]] \begin{aligned} & 900(1+\mathrm{i})+333.12(1+1 / 2 * \mathrm{i})-400(1+1 / 6 * \mathrm{i})=800 \\ & \Rightarrow 999.89^* \mathrm{i}=-33.12 \\ & \Rightarrow \mathrm{i}=-.033 \end{aligned} [[/math]]

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