The difference between simple interest and compound interest of a

Question

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

IanStewart · Accepted Answer

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?

KarishmaB · Answer

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/

Bunuel · Answer

Check other  Compound Interest Problems  in our  Special Questions Directory .

reto · Answer

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

rohit8865 · Answer

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

u1983 · Answer

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

YazedMA · Answer

Simple is 20%+20%=40% and compound is 1.2^2 = 1.44 so the difference is 4%. Thus 4%x=48 --> x=1200

sanjna2023 · Answer

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

shreyasaxena2301 · Answer

Bunuel · Answer

4. Percents and Iterest 
     Theory   
 Math: Number Theory - Percents 
 Percentages, Interest and More 
     Questions   
 Compound Interest Problems 
 DS Questions 
 PS Questions

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

Hope it helps.

AnkithaSrinivas · Answer

the question is not clear - is it asking for sum of money or sum of CI and SI?

Abhishek009 · Answer

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)

nyota.benson · Answer

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
translates to :- CI = P **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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