Bill has been adding funds to his investment account each year for the past 3 years. He started with an initial investment of $1,000. After earning a 10 percent return the first year, he added $3,000 to his portfolio. In this year his investments lost 5 percent. Undeterred, Bill added $2,000 the next year and earned a 2 percent return. Last year, discouraged by the recent results, he only added $500 to his portfolio, but in this final year his investments earned 8 percent. What was Bill's dollar-weighted average return for his investments?

2.96% will be effective rate of the investment

Explanation:

First year:

1,000 x 1 + 10%) =1,100

Second year:

1,100 + 3,000= 4,100 invesmtent balance

4,100 x (1  - 5%) =3,895

Third year:

3,895 + 2,000 = 5,895

5,895 x (1 + 2%) = 6012.9

Fourth year:

6012.9+ 500 = 6512.9

6,512.9 x (1+ 8%)  =  7033.932

We calcualte rate that is equivalent with the following cash flow:

We solve using excel goal seek

0.029646151

a progressive tax is a tax that imposes a lower tax rate on low-income earners compared to those with a higher income, making it based on the taxpayer's ability to pay. that means it takes a bigger percentage from high income earners than it does from low income people.