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The difference between simple interest and compound interest of a

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balamoon
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The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   28 May 2015, 12:12
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The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000
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C
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IanStewart
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   28 May 2015, 12:59
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Simple interest is applied only to the initial investment. So if you invest for 2 years at 20% simple annual interest, the value of the investment will increase by 40%.

If instead we compound 20% interest annually, then we multiply the value of the investment by 1.2 each year, so we multiply by (1.2)^2 = 1.44 over two years. So in this case, the value of the investment will increase by 44%.

These returns differ by 4 percentage points, so the additional money we earn in the compounded case is 4% of our initial investment. If the actual difference is $48, then $48 is 4% of the investment, so $12 is 1%, and $1200 is the answer.

I don't like the wording of the problem though. It's not clear what the question means, for a few reasons. For example, it's confusing to call an amount of money a 'sum', because that suggests we're adding things together, which we're not doing here. Where are these questions from?
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KarishmaB
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   28 May 2015, 20:39
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balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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Simple and compound interest earned in the first year are the same (assuming annual compounding). Difference arises between simple and compound interest in the second year because only in case of compound interest, we earn interest on previous year's interest.

20% of (Year 1 Interest) = 20% of (20% of Principal) = 48
Principal = $1200
Answer (C)

For more on SI, CI concepts, check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... imple-one/
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Bunuel
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   29 May 2015, 04:43
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balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   17 Jun 2015, 03:57
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balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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Be lazy and plug in. Start in the middle with AC C:

Compound Interest (Simple Interest)
Year 1 = 1440 (1440)
Year 2 = 1728 (1680)

Whoops, that's already the answer since 1728 - 1680 = 48
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   25 May 2016, 13:32
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balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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Please note that CI is greater than SI (if counted for >1 year) & equal for same year
So the difference given in stem must be CI-SI=48.
Let x be amount invested then
SI=2x/5
CI =x(1+20/100)^(2)-x------->(36x/25)-x------->11x/25
Difference=11x/25-2x/5-------->x/25
As given x/25=48
x=25*48
x=1200
Ans c
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   25 Apr 2018, 19:54
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balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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Although there are various nice solutions already posted, I would like solve this issue as :

Lets assume the sum is 100.
SI at 20% per annum for 2 years = 100 * .2 *2= 40

CI Then SI at 20% per annum for 2 years = \(100( 1+.2)^2 - 100\) = \(100 (1.2)^2 -100\) = \(100*1.44-100\) = \(144-100\) = 44

4 is the difference when amt is 100
or 1 is the difference when amt is \frac{100}{4}
Hence, 48 is the difference when amount is = \(\frac{100}{4} *48\)=\(100*12\)= 1200 Hence C
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YazedMA
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   27 Dec 2019, 14:19
Simple is 20%+20%=40% and compound is 1.2^2 = 1.44 so the difference is 4%. Thus 4%x=48 --> x=1200
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   01 Jul 2020, 11:04
If you are familiar with the concept of SI and CI, we know that since the Principal amount for both cases is the same with same rate of interest, the interest earned after Year 1 for both cases i.e. Simple interest and Compound Interest will be the same. (Incase you are unfamiliar with the concept, you must read the theory shared by Bunuel.)
I calculated backwards,
Year 1 interest*20/100=48 =>Year 1 interest = 240
Since we know the interest earned after year 1 => Principal*20/100=240 => Principal=1200
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   11 Sep 2020, 01:49
Bunuel wrote:
balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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can anyone please tell complete formulas of SI and CI with explanation of concepts. I am facing trouble in these questions, thanks in advance.

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Bunuel
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   11 Sep 2020, 02:03
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shreyasaxena2301 wrote:
Bunuel wrote:
balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

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can anyone please tell complete formulas of SI and CI with explanation of concepts. I am facing trouble in these questions, thanks in advance.

Check other Compound Interest Problems in our Special Questions Directory.




4. Percents and Iterest



For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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AnkithaSrinivas
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   18 Jun 2021, 02:41
the question is not clear - is it asking for sum of money or sum of CI and SI?
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   09 Jan 2024, 08:28
balamoon wrote:
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is

(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000

CI for 2 years is 20 + (20% of 20 + 20) = 44
SI for 2 years is 40

Diff is 4

Now, Principal will be 48/4*100 = 1200, Answer will be (C)
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Re: The difference between simple interest and compound interest of a [#permalink] The difference between simple interest and compound interest of a   10 Jan 2024, 23:48
Despite other good answers, this also is direct;

Simple Interest:
SI = p * R * T

which translates to SI = P * 0.2 * 2
= 0.4P ...................(1)

Compound Interest:
CI = [P(1 + R)**T] - P
translates to :- CI = P[1+0.2]**2 - P
= 1.44P - P
= O.44P .......................(2)

Difference between CI - SI = $48
** knowing that compound interest is greater than simple interest.
therefore:
0.44p - 0.4p = $48
0.04p = $48

p = $48/0.04
p = $4800/4

p = $1200

Hence Ans C
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Re: The difference between simple interest and compound interest of a [#permalink]
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