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

Question

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

pushpitkc · Accepted Answer

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)

BrentGMATPrepNow · Answer

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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hellosanthosh2k2 · Answer

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

ScottTargetTestPrep · Answer

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

EMPOWERMathExpert · Answer

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

The final answer is

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D

.

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ShenotShih1017 · Answer

250 = x + 5XY/100 
270 = X + 7XY/100

27,000 = 100X +7XY
25,000= 100X + 5XY

(subtract the two equations):

2000 = 2XY

1000 = XY

The only answer choice that is the sum of two numbers that multiply to 1000 is 205.

bumpbot · Answer

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

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