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Percents and Interest Problems

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by swerve » Fri Mar 13, 2020 6:51 am

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A

B

C

D

E

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On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecap rises 5% , midcap rises 10%, and smallcap rises 15% in the Antarctic stock market; however, 2011, largecap fall 10% and midcaps fall 20%, while smallcap rises \(x\)% in Antarctica. If on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then \(x\) is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

The OA is D

Source: Manhattan Prep
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Source: — Problem Solving |

swerve wrote:
Fri Mar 13, 2020 6:51 am
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecap rises 5% , midcap rises 10%, and smallcap rises 15% in the Antarctic stock market; however, 2011, largecap fall 10% and midcaps fall 20%, while smallcap rises \(x\)% in Antarctica. If on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then \(x\) is between

A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60

The OA is D

Source: Manhattan Prep
Let’s let the amount Dave invested on January 1, 2010 be $1,000. So he invested $700 in largecaps, $200 in midcaps, and $100. in smallcaps.

After two years, the amount he has 700 * 1.05 * 0.9 = $661.5 in largecaps, 200 * 1.1 * 0.8 = $176 in midcaps and 100 * 1.15 * (1 + x/100) = 115(1 + x/100) dollars in smallcaps.

Since the total amount is the same as two years earlier, we have:

661.5 + 176 + 115(1 + x/100) = 1,000

115(1 + x/100) = 162.5

1 + x/100 = 1.413

x/100 = 0.413

x = 41.3

Answer: D

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