A person invests an equal amount of money in two investment schemes fo

Question

A person invests an equal amount of money in two investment schemes for two years. In the first investment scheme, he earns an interest at 10% p.a. simple interest and in the second investment scheme he earns an interest at 10% p.a. compounded annually. What is the difference in the interest earned under the two investment schemes at the end of the second year?

(1) The amount the person invests in each scheme is $10,000.
(2) He earns an interest of $1000 in the 1 scheme at the end of 1 year.

Show Answer

Official Answer

D

(1) The amount the person invests in each scheme is $10,000.
(2) He earns an interest of $1000 in the 1 scheme at the end of 1 year.

yashikaaggarwal · Answer

IMO D

Statement 1: 
SI (for 2 years) = P*R*T/100
10,000*10*2/100 = 2000
(For 2 years)
CI = P(1+r/100)^t -P
CI = 10,000(1+0.1)^2-10,000
CI = 10,000(1.1)^2-10,000
CI = 10,000(1.21)-10,000
CI = 12100-10,000
CI = 2100
CI-SI = 2100-2000 = 100 (sufficient)

Statement 2: SI (for 1 year) = PRT/100
1000=P*10*1/100
P=10,000
SI (for 2 years) = P*R*T/100
10,000*10*2/100 = 2000
(For 2 years)
CI = P(1+r/100)^t -P
CI = 10,000(1+0.1)^2-10,000
CI = 10,000(1.1)^2-10,000
CI = 10,000(1.21)-10,000
CI = 12100-10,000
CI = 2100
CI-SI = 2100-2000 = 100 (sufficient)

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NitishJain · Answer

IMO  D

Given: r= 10% for both schemes, t=2 Let Amount invested = P

SI =  \frac{(P*10*2)}{100}  =  \frac{20P}{100}

CI = P(1 +  \frac{10}{100} )^2 - P
 =  \frac{121P}{100}  - P =  \frac{21P}{100}

Difference in Interest =  \frac{21P}{100}  -  \frac{20P}{100}  =  \frac{P}{100}

If we get P, it will be sufficient

(STATEMENT 1): The amount the person invests in each scheme is $10,000. P= 10,000.  SUFFICIENT

(STATEMENT 2): He earns an interest of $1000 in the 1 scheme at the end of 1 year.

Case 1: interest of $1000 in the First scheme = 
SI = 1000 =  \frac{(P*10*1)}{100} 
P = 10000

Case 2: interest of $1000 in any Second scheme =  INSUFFICIENT , and the answer will be  A . ( Statement is sufficient )
CI = 1000 = P (1+ \frac{10}{100} ) - P =  \frac{P}{10} 
P= 10000

In both cases P is same ,  SUFFICIENT

CrackverbalGMAT · Answer

A person invests an equal amount of money in two investment schemes for two years. In the first investment scheme, he earns an interest at 10% p.a. simple interest and in the second investment scheme he earns an interest at 10% p.a. compounded annually. What is the difference in the interest earned under the two investment schemes at the end of the second year?

(1) The amount the person invests in each scheme is $10,000.
(2) He earns an interest of $1000 in the 1 scheme at the end of 1 year.

Show Answer

Official Answer

D

In the above case, CI earned will be greater than SI because, In C.I, the first-year interest amount will also start to gain interest in the second year-end evaluation.

First year Interest = P * r/100 * 1= P*r/100

Interest you get from First year interest in the end of second year = r% of (First year interest )
=r% of ( P* \frac{r}{100} ) =P*  \frac{r^2}{100^2}

We can conclude that Difference between CI and SI for 2 years = P*  \frac{r^2}{100^2}

Here, r is given as 10% 
So the difference =  P* \frac{10^2}{100^2}  =  \frac{P}{100} .
So in order to answer the question stem, we need to find the value of P.

(1) The amount the person invests in each scheme is $10,000.
The value of P is given in St.1 So its clearly sufficient.

(2) He earns an interest of $1000 in the 1 scheme at the end of 1 year.
Remember that CI and SI at the end of 1 year will be the same. They will change only after the end of 2nd year on wards.

1000 = P * 10/100 * 1

P = 10,000

St 2 alone is also sufficient.

Option D is the answer.

Thanks,
  Clifin J Francis,
GMAT SME

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