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In 2001, John invests x dollars in a special account that yields y%

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In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post 28 Jul 2017, 07:50
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In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210

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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post 28 Jul 2017, 10:22
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The interest accrued over 2 years is 20$ which is 10$ per year
Since this amount x had been invested for 7 years, the total interest is 70$

Total = Interest + Principal(x)
Principal(x) = Total - Interest = 270 - 70 = 200
Since 10 is 5% of 200 , y=5
Therefore the amount was invested at an annual rate of 5%(which is y) and amount invested(x) = 200

Sum of x and y = 200 + 5 = 205(Option D)
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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post 21 Aug 2017, 08:41
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Bunuel wrote:
In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210


With simple interest, the annual interest accrued is the SAME each year

We're told that in 2 years (from 2006 to 2008), the investment increases by $20 (from $250 to $270)
So, EACH YEAR, the investment increases by $10
There are 7 years from 2001 (the year of John's initial investment of x dollars) to 2008 (when John's investment reaches $270)
In those 7 years, John's ANNUAL interest is $10. So, the TOTAL interest accrued in 7 years = (7)($10) = $70

So, in 2001, John's initial investment = $270 - $70 = $200 So, x = 200

We now know that: John's initial investment = $200. The ANNUAL interest is $10.
10/200 = 5/100 = 5% So, the annual interest RATE = 5%. In other words, y = 5

So, x + y = 200 + 5 = 205

Answer: D

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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post 07 Feb 2018, 12:13
one quick approach (might not work always)

given amount increased by 20$ from 250 (2006) to 270 (2008)
so 2xy/100 = 20
=> xy = 1000
quickly scanning through choice and pick x = 200, y = 5 , option D fits well
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Re: In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post 23 Sep 2018, 15:41
Bunuel wrote:
In 2001, John invests x dollars in a special account that yields y% simple interest annually. If he has $250 in his account in 2006 and in 2008 he has $270 in his account, what is x + y?

(A) 5

(B) 25

(C) 200

(D) 205

(E) 210


Since he has $250 in his account in 2006 and $270 in 2008, it must be true that the amount of interest is $20 during these two years. Since it’s a simple interest, it must mean the amount of interest is $10 per year.

Therefore, in 2001, 5 years before 2006, it must have accumulated $50 in interest, which means the amount in 2001 is $200. So x = 200. Since 10/200 = 5/100 = 5%, y = 5. Therefore, x + y = 205.

Answer: D
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In 2001, John invests x dollars in a special account that yields y%  [#permalink]

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New post Updated on: 26 Sep 2018, 23:52
To start, we can find the amount earned from 2006 to 2008:\(\$270 - \$250 = \$20\).

This means that John earned \(\$20\) in \(2\) years, so the interest earned per year is \(\$20 \div 2 = \$10 \ per \ year\).

Using the rate of \(\$10/year\), we can find the amount invested in 2001 by subtracting \(\$10\) every preceding year.

Image

Since \(x\) is the amount invested in 2001, then \(x = 200\).

To find the annual interest rate, we use \(\$200\) as the principal.

Rate per year = Interest per year \(\div\) Principal Rate per year \(= \$10 \div \$200
\)

Rate per year = \(0.05\) or \(5\%\)

Since \(y\%\) is the annual interest rate, then \(y = 5\).

Thus, the value of \(x + y = 200 + 5 = 205\).

The final answer is .

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Originally posted by EMPOWERMathExpert on 26 Sep 2018, 23:34.
Last edited by Bunuel on 26 Sep 2018, 23:52, edited 1 time in total.
Fixed external link issue.
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In 2001, John invests x dollars in a special account that yields y% &nbs [#permalink] 26 Sep 2018, 23:34
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