Johnrohit wrote:Judy invests a sum of money in a bank deposit at Bank A at 10%, interest compounded annually. An equal sum of money is invested in a bank deposit for 20% in Bank B compounded annually. After 2 years, the difference between the amount in the Bank A and B is $92. What is the sum of money invested in bank deposit of Bank B??
$400
$350
$800
$200
We can PLUG IN THE ANSWERS, which represent the amount invested in each account.
After 2 years, B-A = $92 -- an INTEGER value.
In A, the amount each year increases by 10%, implying that over 2 years the amount in A will be multiplied by 11/10 two times:
(11/10)(11/10)A = (121/100)A.
Implication:
The correct answer choice will be a MULTIPLE OF 100, so that the amount in A after 2 years will be an integer value.
Of the 3 multiples of 100 in the answer choices -- 200, 400, and 800 -- start with the MIDDLE value:
Answer choice A: 400
Bank A:
Amount after 1 year = 400 + (10/100)(400) = 400 + 40 = 440.
Amount after 2 years = 440 + (10/100)(440) = 440 + 44 = 484.
Bank B:
Amount after 1 year = 400 + (20/100)(400) = 400 + 80 = 480.
Amount after 2 years = 480 + (20/100)(480) = 480 + 96 = 576.
Resulting difference:
B-A = 576 - 484 = 92.
Success!
The correct answer is
A.
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