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How much of $5,000 savings should be invested in an account that yield

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How much of $5,000 savings should be invested in an account that yield  [#permalink]

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New post 22 Jan 2018, 01:27
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A
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E

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Question Stats:

79% (02:05) correct 21% (02:18) wrong based on 43 sessions

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How much of $5,000 savings should be invested in an account that yields 5% simple annual interest, if the rest will be invested in an account that yields 7% simple annual interest and the desired return after a year is exactly 6.5% on the entire $5,000?

A. $2,500
B. $2,250
C. $2,000
D. $1,750
E. $1,250

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Re: How much of $5,000 savings should be invested in an account that yield  [#permalink]

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New post 22 Jan 2018, 05:10
Bunuel wrote:
How much of $5,000 savings should be invested in an account that yields 5% simple annual interest, if the rest will be invested in an account that yields 7% simple annual interest and the desired return after a year is exactly 6.5% on the entire $5,000?

A. $2,500
B. $2,250
C. $2,000
D. $1,750
E. $1,250


The question can be solved using weighted Average method or by forming a simple equation. Here is the solution that I like to share with reader

Let, $x is to be invested @5%
i.e. $(5000-x) is to be invested @7%

i.e. Total Interest = (5/100)*x + (7/100)*(5000-x) = (6.5/100)*5000

Solving this equation we get, 5x + 35000 - 7x = 32500

i.e. 2x = 2500

i.e. x = $1250


Answer: option E
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Re: How much of $5,000 savings should be invested in an account that yield  [#permalink]

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New post 22 Jan 2018, 09:11
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Bunuel wrote:
How much of $5,000 savings should be invested in an account that yields 5% simple annual interest, if the rest will be invested in an account that yields 7% simple annual interest and the desired return after a year is exactly 6.5% on the entire $5,000?

A. $2,500
B. $2,250
C. $2,000
D. $1,750
E. $1,250
Attachment:
Capture.PNG
Capture.PNG [ 3.73 KiB | Viewed 776 times ]


So, Amount invested at 5% Simple Interest is \(\frac{1}{4}*5000\) = \(1250\) , answer will be (E)

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Re: How much of $5,000 savings should be invested in an account that yield  [#permalink]

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New post 23 Jan 2018, 08:55
Bunuel wrote:
How much of $5,000 savings should be invested in an account that yields 5% simple annual interest, if the rest will be invested in an account that yields 7% simple annual interest and the desired return after a year is exactly 6.5% on the entire $5,000?

A. $2,500
B. $2,250
C. $2,000
D. $1,750
E. $1,250



We can create a weighted average equation, in which x = the amount invested at 5% and 5,000 - x = the amount invested at 7%.


0.05x + 0.07(5,000 - x) = 0.065(5000)

0.05x + 350 - 0.07x = 325

-0.02x = -25

x = 1,250

Answer: E
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Re: How much of $5,000 savings should be invested in an account that yield  [#permalink]

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Re: How much of $5,000 savings should be invested in an account that yield   [#permalink] 10 Jun 2019, 22:41
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