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A man invested two equal sums of money in two banks at simple interest

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A man invested two equal sums of money in two banks at simple interest  [#permalink]

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New post 27 Sep 2018, 04:38
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Question Stats:

60% (01:48) correct 40% (02:06) wrong based on 15 sessions

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A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between $120 and $140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest?

(A) $130
(B) $135
(C) $137
(D) $154
(E) $162

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A man invested two equal sums of money in two banks at simple interest  [#permalink]

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New post 27 Sep 2018, 06:28
Bunuel wrote:
A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between $120 and $140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest?

(A) $130
(B) $135
(C) $137
(D) $154
(E) $162


Difference of interest after 1 year = 20%-10% = 10% of principal
Difference of interest after 2 years = 40%-20% = 20% of principal

i.e. 20% of half of the sum is between 120 and 140
i.e. Sum is between 1200 and 1400

For 1200 distributed in two accounts with sum 600 each
Interest @ 10% after two years \(= (1.1)^2*600-600 = 126\)
Interest @ 20% after two years \(= (1.2)^2*600-600 = 264\)
Difference = 138

For 1400 distributed in two accounts with sum 700 each
Interest @ 10% after two years \(= (1.1)^2*700-700 = 147\)
Interest @ 20% after two years \(= (1.2)^2*700-700 = 161\)


Only value available in options that falls between 147 and 161 is 154 hence

Answer: Option D
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Re: A man invested two equal sums of money in two banks at simple interest  [#permalink]

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New post 29 Sep 2018, 23:03
Bunuel wrote:
A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between $120 and $140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest?

(A) $130
(B) $135
(C) $137
(D) $154
(E) $162


Responding to a pm:
The difference between the interests earned in two years is in the range $120 - $140. So the answer will be obtained in a range too. We need to find the value that falls in this range.
Let's take the middle value and find the value closest to it.

Take the difference in SI of two years to be say $130. So each year extra SI will be $65 (because rate in second case is 20%, 10% more than the rate of 10%).
$65 is 10% of the principal so principal would be $650.

Diff in interest earned in CI on $650 at 10% interest vs 20% interest:
On $650, CI earned at 10% in 2 years = 65 + 65 + 6.5
On $650, CI earned at 20% in 2 years = 130 + 130 + 26
The difference is about $150.
$150 is going to lie in the middle of our acceptable range so $154 should certainly lie in this range.

Answer (D)
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Re: A man invested two equal sums of money in two banks at simple interest &nbs [#permalink] 29 Sep 2018, 23:03
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