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# The difference, after two years, between compound interest and simple

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Math Expert
Joined: 02 Sep 2009
Posts: 50001
The difference, after two years, between compound interest and simple  [#permalink]

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27 Sep 2018, 05:35
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35% (medium)

Question Stats:

75% (01:19) correct 25% (03:35) wrong based on 20 sessions

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The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is \$18. If the simple interest accumulated on the sum after two years is \$180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

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Re: The difference, after two years, between compound interest and simple  [#permalink]

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27 Sep 2018, 12:32
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Bunuel wrote:
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is \$18. If the simple interest accumulated on the sum after two years is \$180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

We'll use the underlying logic behind interest to create a simple equation, without bothering with variables.
This is a Logical approach.

The only difference between the compound and simple interest is that the compound interest was calculated twice - once at the end of the first year and once at the end of the second year.
So, the \$18 difference must be due to the second year's interest earned from the first year's interest.
Since 2 years of simple interest is \$180, one year is \$90 so 90*rate = 18 meaning that our interest rate is 18/90 = 2/10 = 20%

Note that understanding the underlying logic created an extremely simple calculation: 18 divided by (180/2), as opposed to something full of variables.
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Re: The difference, after two years, between compound interest and simple  [#permalink]

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28 Sep 2018, 04:53
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If simple interest was 180\$, that means simple interest must have been 90\$ per year. So, the difference in 18\$ must have ocurred due to the interest in interest, i.e. (90*x)/100 = 18, x = 20%.

IMO D.
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Re: The difference, after two years, between compound interest and simple  [#permalink]

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30 Sep 2018, 11:57
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , \$18 is for 2 year , how you can take \$90*x/100 = \$18
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The difference, after two years, between compound interest and simple  [#permalink]

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30 Sep 2018, 22:03
vipulshahi wrote:
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , \$18 is for 2 year , how you can take \$90*x/100 = \$18

Sure, when you calculate simple interest and compound interest for any given amount, the interest for the first year remains the same. Example, you have 100\$ on both SI and CI for 2 years @ 10%, for the first year both will earn an interest of 10\$. But for the second year, SI will again earn 10\$, but CI will earn 11\$. Why? because now the amount for CI becomes the amount initially invested plus the interest earned i.e. 100\$ + 10\$ = 110\$. Since the interest earned is not taken out but added in the principal amount invested for CI, the difference starts coming from second year onwards.

Hope that helps.
The difference, after two years, between compound interest and simple &nbs [#permalink] 30 Sep 2018, 22:03
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