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