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16 Sep 2014, 00:35
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A construction project is planned to be completed in 5 years, with investments made at the start of each year. The amount invested in each succeeding year is twice that of the previous year. Approximately what percentage of the total cost of the project will be invested in the first year?
A. 12.5%
B. 10%
C. 8.25%
D. 5%
E. 3%
A. 12.5%
B. 10%
C. 8.25%
D. 5%
E. 3%
16 Sep 2014, 00:35
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Official Solution:
A construction project is planned to be completed in 5 years, with investments made at the start of each year. The amount invested in each succeeding year is twice that of the previous year. Approximately what percentage of the total cost of the project will be invested in the first year?
A. 12.5%
B. 10%
C. 8.25%
D. 5%
E. 3%
To calculate the percentage of the total cost invested in the first year of a 5-year construction project, we can assume an investment amount of \($1\) in the first year, and then calculate the investment amounts for the subsequent years by doubling the previous year's investment. Adding up these investments gives a total of \(1+2+4+8+16=$31\). The investment in the first year, therefore, is \(\frac{1}{31}\) of the total cost, which is about 3%.
Answer: E
A construction project is planned to be completed in 5 years, with investments made at the start of each year. The amount invested in each succeeding year is twice that of the previous year. Approximately what percentage of the total cost of the project will be invested in the first year?
A. 12.5%
B. 10%
C. 8.25%
D. 5%
E. 3%
To calculate the percentage of the total cost invested in the first year of a 5-year construction project, we can assume an investment amount of \($1\) in the first year, and then calculate the investment amounts for the subsequent years by doubling the previous year's investment. Adding up these investments gives a total of \(1+2+4+8+16=$31\). The investment in the first year, therefore, is \(\frac{1}{31}\) of the total cost, which is about 3%.
Answer: E
23 Feb 2023, 03:00
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
