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23 May 2022, 06:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
87% (02:02) correct
13%
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wrong
based on 85
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Bob invested $1,000 at 10 percent annual interest, compounded annually, and Joe invested $2,000 at 5 percent annual interest, compounded annually. The total amount of interest earned by Bob's investment in the first 2 years was how much greater than the total amount of interest earned by Joe's investment in the first 2 years?
A. $2
B. $3
C. $4
D. $5
E. $10
A. $2
B. $3
C. $4
D. $5
E. $10
23 May 2022, 06:51
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Bunuel
Bob starts with $1000. He earns 10% interest in year one. 10% of $1000 is $100, so he has $1100 at the end of year one. He earns 10% interest in year two. 10% of $1100 is $110. He earned $100 interest in year one and $110 interest in year two. Add those together for a total of $210.
Joe starts with $2000. He earns 5% interest in year one. 5% of $2000 is $100, so he has $2100 at the end of year one. He earns 5% interest in year two. 5% of $2100 is $105. He earned $100 interest in year onw and $105 interest in year two. Add those together for a total of $205.
Bob earned $210 and Joe earned $205.
Answer choice D.
Note that we did NOT need to calculate how much either guy had at the end of year two in order to get to the right answer. Pay attention to what you're solving for in order to save unnecessary steps!!
23 May 2022, 07:03
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Both investments earn the same $100 on the initial investment each year. The only reason they earn different amounts is because of the compounding; Bob earns, in the second year, 10% on top of the $100 of interest he earned in year one, while Joe only earns 5% on top of the $100 of interest he earned in year one, so the difference is $5.
01 Aug 2023, 16:17
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Bob interest after 2 years
(1 + 10/100)^2
1.1^2
1.21
Interest = 0.21 x 1000 = 210
Joe's after 2 years
(1 + 5/100)^2
1.05^2
1.1025
Interest
0.1025 x 2000
= 205
Difference
210-205 = 5
GMAT quant instructor Lagos Nigeria
Posted from my mobile device
(1 + 10/100)^2
1.1^2
1.21
Interest = 0.21 x 1000 = 210
Joe's after 2 years
(1 + 5/100)^2
1.05^2
1.1025
Interest
0.1025 x 2000
= 205
Difference
210-205 = 5
GMAT quant instructor Lagos Nigeria
Posted from my mobile device
