# Aptitude - Compound Interest

### Exercise :: Compound Interest - Data Sufficiency 3.1

In each of the following questions, a question is asked and is followed by three statements. While answering the question, you may or may not require the data provided in all the statements. You have to read the question and the three statements and then decide whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question. The answer number bearing the statements, which can be dispensed with, if any, while answering the question is your answer.

1.

 Mr. Gupta borrowed a sum of money on compound interest. What will be the amount to be repaid if he is repaying the entire amount at the end of 2 years? I. The rate of interest is 5 p.c.p.a. II. Simple interest fetched on the same amount in one year is Rs. 600. III. The amount borrowed is 10 times the simple interest in 2 years.

 A. I only B. III only C. I or II only D. II and Either I or III only E. All I, II and III are required

Explanation:

I. gives, Rate = 5% p.a.

II. gives, S.I. for 1 year = Rs. 600.

III. gives, sum = 10 x (S.I. for 2 years).

Now I, and II give the sum.

For this sum, C.I. and hence amount can be obtained.

Thus, III is redundant.

Again, II gives S.I. for 2 years = Rs. (600 x 2) = Rs. 1200.

Now, from III, Sum = Rs. (10 x 1200) = Rs . 12000.

 Thus, Rate = 100 x 1200 = 5% p.a. 2 x 12000

Thus, C.I. for 2 years and therefore, amount can be obtained.

Thus, I is redundant.

Hence, I or III redundant.

2.

 What is the compound interest earned at the end of 3 years? I. Simple interest earned on that amount at the same rate and for the same period is Rs. 4500. II. The rate of interest is 10 p.c.p.a. III. Compound interest for 3 years is more than the simple interest for that period by Rs. 465.

 A. I and II only B. II and III only C. I and III only D. I and Either II or III only E. Any two of the three

Explanation:

I. gives, S.I for 3 years = Rs. 4500.

II. gives, Rate = 10% p.a.

III. gives, (C.I.) - (S.I.) = Rs. 465.

Clearly, using I and III we get C.I. = Rs. (465 + 4500).

Thus, II is redundant.

 Also, from I and II, we get sum = 100 x 4500 = 15000. 10 x 3

Now C.I. on Rs. 15000 at 10% p.a. for 3 years may be obtained.

Thus, III is redundant. Either II or III is redundant.