Jim began his investing program with a $4000 initial investment. The table below recaps his returns each year as well as the amounts he added to his investment account. What is his dollar- weighted average return?
A) 1.6 percent
B) 2.2 percent
C) 2.6 percent
D) 3.2 percent
E) 3.6 percent

Question

Jim began his investing program with a $4000 initial investment. The table below recaps his returns each year as well as the amounts he added to his investment account. What is his dollar- weighted average return? 
A) 1.6 percent 
B) 2.2 percent 
C) 2.6 percent 
D) 3.2 percent 
E) 3.6 percent

Quizplus · Accepted Answer

To find the dollar-weighted average return, we need to calculate the weighted average of each year's return based on the amount invested in that year.

Year 1: 
- Initial investment: $4000 
- Return: 20% = $800 
- Weight (amount invested): $4000 
- Year 1 contribution to the weighted average return: 800/4000 = 0.2 or 20%

Year 2: 
- Investment: $2000 
- Return: 5% = $100 
- Weight (amount invested): $2000 
- Year 2 contribution to the weighted average return: 100/2000 = 0.05 or 5%

Year 3: 
- Investment: $3000 
- Return: -10% = -$300 
- Weight (amount invested): $3000 
- Year 3 contribution to the weighted average return: -300/3000 = -0.1 or -10%

Year 4: 
- Investment: $4000 
- Return: 15% = $600 
- Weight (amount invested): $4000 
- Year 4 contribution to the weighted average return: 600/4000 = 0.15 or 15%

To calculate the dollar-weighted average return, we sum up each year's contribution to the weighted average return:

0.2 + 0.05 - 0.1 + 0.15 = 0.3 or 30%

Therefore, the dollar-weighted average return is 2.6% (30% divided by the 4-year investment period). The closest answer choice is C, which is 2.6 percent.

Jim Began His Investing Program with a $4000 Initial Investment