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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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28 Jul 2017, 07:50
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13
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Difficulty:

65% (hard)

Question Stats:

62% (02:26) correct 38% (02:59) wrong based on 190 sessions

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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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28 Jul 2017, 10:22
3
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) _________________ You've got what it takes, but it will take everything you've got CEO Joined: 11 Sep 2015 Posts: 3431 Location: Canada Re: In 2001, John invests x dollars in a special account that yields y% [#permalink] ### Show Tags 21 Aug 2017, 08:41 1 Top Contributor 2 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

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

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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 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4920 Location: United States (CA) Re: In 2001, John invests x dollars in a special account that yields y% [#permalink] ### Show Tags 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.

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

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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.

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 $$x + y = 200 + 5 = 205$$.

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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.
In 2001, John invests x dollars in a special account that yields y%   [#permalink] 26 Sep 2018, 23:34
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