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A $500 investment and a $1,500 investment have a combined [#permalink]

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06 Oct 2013, 05:27

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A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

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06 Oct 2013, 05:47

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jlgdr wrote:

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

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06 Oct 2013, 06:31

jlgdr wrote:

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

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29 Dec 2013, 03:35

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jlgdr wrote:

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

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Re: A $500 investment and a $1,500 investment have a combined [#permalink]

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Alternative 30-second approach:

The $500 and $1500 investments are in the ratio 1:3, hence the $1500 investment is responsible for 3/4 of the total investment returns. We know the total average return is 8.5% and the $500 investment yields a 7% return, which is 1.5% away from the average.

Hence, the $1500 must be 1/3 of the distance away from the average as compared to the $500 investment. 1/3 of 1.5% is 0.5%.

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27 Jun 2017, 02:52

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jlgdr wrote:

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

Re: A $500 investment and a $1,500 investment have a combined [#permalink]

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27 Jun 2017, 13:29

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

Total Amount = $500 + $1,500 = $2,000

Interest on Total Amount:

\(= 2000 * \frac{8.5}{100}\)

\(= $170\)

Interest Amount on $500 \(= 500 * \frac{7}{100}\)

\(= $35\)

Interest Amount for $500 + Interest Amount for $1500 = Interest Amount for $2000

35 + Interest Amount for $1500 \(= 170\)

Interest Amount for $1500 \(= 170 - 35\)

Interest Amount for $1500 \(= 135\)

135 is what % of 1500?

\(= \frac{135}{1500} * 100\)

= 9%

Hence, Answer is A _________________

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A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1 ,500 investment have?

(A) 9% (B) 10% (C) 10 5/8% (D) 11% (E) 12%

The ratio of investments is 500:1,500 = 1:3.

The deviation from the average return from $500 investment and $1,500 investment must be in the ration 3:1.

$500 investment return has the deviation from the mean of 8.5-7=1.5%, thus $1,500 investment return must have the deviation from the mean equal to 0.5%, which means that $1 ,500 investment has 8.5+0.5=9% yearly return.