Bunuel wrote:

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

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 $ amountsWe 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