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29 Jun 2018, 02:04
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D
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Difficulty:
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Question Stats:
70% (03:06) correct
30%
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wrong
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Last year, Melania had a total of $20,000 invested in two mutual funds, Capital Growth Fund and Venture Index Fund. At the end of the year, she analyzed her investments and found that her earnings on her shares of Capital Growth Fund were three times half of her earnings on her investment in Venture Index Fund. If she earned a total of $1,250 on her investments in the two funds, and had three times as much money invested in Capital Growth Fund as in Venture Index Fund, what percent interest did Melania earn on her investment in Venture Index Fund?
(percent interest = \(\frac{earnings}{investment}*100\))
A. .075
B. .01
C. 7.5
D. 10
E. 500
(percent interest = \(\frac{earnings}{investment}*100\))
A. .075
B. .01
C. 7.5
D. 10
E. 500
29 Jun 2018, 02:21
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Bunuel
Formula used: percent interest = \(\frac{earnings}{investment}*100\)
If the earning on the Venture Index Fund is \(x\), the earnings on the Capital Growth Fund is \(\frac{3x}{2}\)
We know that \(x + \frac{3x}{2} = 1250\)(since she earned $1250 from her investment on both the funds)
Simplifying the equation, we get \(\frac{5x}{2} = 1250\) -> \(x = \frac{2500}{5} = $500\)
Since she had 3 times as much money invested in the Capital Growth fund as in the Venture Index
fund, the ratio of amounts invested in the funds is 3:1. Here, we are concerned about the percent
increase in the Venture Index Fund, the investment in the Venture Index fund is \(\frac{1}{1+3}*20000 = $5000\)
Therefore, the percent interest on her investment in the Venture Index Fund is \(\frac{500}{5000} * 100 = 10\)(Option D)
29 Jun 2018, 08:08
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Bunuel
Great question.
Let Capital Growth Fund = \(C\)
Let Venture Index Fund = \(V\)
I. Shortcut
\(V\): percent interest on investment in V?
(Portion/percent of earnings) *
(Portion/percent invested) =
Overall percent interest for that portion
(1) Interest from \(V\) is what percent / portion of earnings
\(C+V=\)total interest earnings
\(C= \frac{3}{2}V\)
\(\frac{C}{V}=\frac{3}{2}\)
\(\frac{C}{V}=(3x:2x)\), thus \(5x\) parts
\(V=\frac{2}{5}\) of earnings
(2) Investment in \(V\) is what percent / portion of total invested?
\(C=3V\), and \(\frac{C}{V}=\frac{3}{1}\)
\((3C:1V)=(3x:1x)\), total parts = \(4x\)
\(V=\frac{1}{4}\) of total invested
(3) Percent interest
(Portion/percent of earnings) *
(Portion/percent of $ invested) =
Overall percent interest for that portion
\((\frac{2}{5}*\frac{1}{4})=\frac{2}{20}=\frac{1}{10}=.10=\) 10 percent
Answer D
II. V's % interest: ratios and $ amounts
We need V's \(\frac{earnings}{investment}\). In parts:
(1) How much of the $1,250 in interest earnings came from investment in \(V\)?
Given: earnings from \(C\) were "three times half" the earnings on investment in \(V\)
\(C= \frac{3}{2}V\)
Combined, investments in \(C\) and \(V\) returned $1,250 in interest earnings
\(C + V=$1,250\)
\(\frac{3}{2}V+V=$1,250\)
\(\frac{5}{2}V=$1,250\)
\(V=($1,250*\frac{2}{5})=$500\)
(2) How much of $20,000 was invested in \(V\)?
\(C+V=20,000\)
She invested 3 times as much money in \(C\) as in \(V\)
\(C=3V\)
\(3V+V=$20,000\)
\(4V=$20,000\)
\(V=$5,000\)
She invested $5,000 of the $20,000 in \(V\)
(3) What percent interest did she earn on investment in \(V\)?
Earnings (interest) from \(V: $500\)
Total money invested in \(V:$5,000\)
Percent interest = \(\frac{earnings}{investment}*100\))
\((\frac{$500}{$5,000}*100)=(.1*100)=10\) percent
Answer D
