# Compound Interest - Aptitude Questions and Answers - RejinpaulPlacement

Directions (Questions 64 to 67) : Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question :
64.
What is the rate of interest p.c.p.a. ? [R.B.I. 2002]

I. An amount doubles itself in 5 years on simple interest.
II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400
III. Simple interest earned per annum is Rs. 2000.

Answer: e) I only or II and III only

Solution:   I. [(P * R * 5)/100] = P
=> R = 20

II. P[1 + (R/100)]^2 - P - [(P * R * 2)/100] = 400
=> PR^2 = 4000000

III. [(P * R * 1)/100] = 2000
=> PR = 200000

(PR^2/PR) = 4000000/200000
=> R = 20

Thus, I only or (II & III) give answer.
65.
A sum of money is put at compound interest. What is the rate of interest?

I. The sum amounts to Rs. 5290 in 2 years.
II. The sum amounts to Rs. 6083.50 in 3 years.
III. The sum is Rs. 4000.
Answer: d) Any two of the three

Solution:   I. P [1 + (R/100)]^2 = 5290 ...... (i)
II. P[1 + (R/100)]^3 = 6083.50 ...... (ii)

On dividing (ii) by (i), we get :
[1 + (R/100)] = 608350/529000 = 23/20
=> R/100 = [(23/20) - 1] = 3/20
=> R = 15
Thus, I and II give answer.

III gives P = 4000.

Putting this value of P in (i), we get the answer.
Putting this value of P in (ii), we get the answer.

(I & II) or (I & III) or (II or III) all give the answer.

Hence, the correct answer is (d)
66.
What will be the compound interest earned on an amount of Rs. 5000 in 2 years? [S.B.I.P.O. 2000]

I. The simple interest on the same amount at the same rate of interest in 5 years in Rs. 2000.
II. The compound interest and the simple interest earned in one year is the same.
III. The amount becomes more than double on compound interest in 10 years.

Solution:   P = Rs. 5000 & T = 2 years.

I. S.I. on Rs. 5000 in 5 years is Rs. 2000
[(5000 * R * 5)/100] = 2000
=> R = 8

Thus, I only gives the answer.
67.
A sum of money is placed at compound interest. In how many years will it amount to sixteen times of itself?

I. The sum doubles itself in 4 years.
II. The sum amounts to eight times of itself in 12 years.
III. The sum amounts to four times of itself in 8 years.
Answer: e) Any one of the three

Solution:   I. P[1 + (R/100)]^4 = 2P
=> [1 + (R/100)]^4 = 2 ...... (i)

II. P [1 + (R/100)]^12 = 8P
=> [1 + (R/100)]^12 = 8 ......(ii)

III. P [1 + (R/100)]^8 = 4P
=> [1 + (R/100)]^8 = 4 ....... (iii)

Let the given sum become 16 times in n years. Then,
P [ 1 + (R/100)]^n = 16P
=> [1 + (R/100)]^n = 16 ...... (iv)

Any one of (i), (ii) and (iii) with (iv) will give the value of n.
Directions (Questions 68 to 70): 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.

68.
What would be the difference between the simple interest and the compound interest on a sum of money at the end of four years?

I. The rate of interest is 5 p.c.p.a.
II. The sum fetches a total of Rs. 2000 as simple interest at the end of 8 years.
III. The difference between the simple interest and the compound interest at the end of 2 years is Rs. 12.50
Answer: c) II or III only

Solution:   I and II will give us, R, S.I. and T.

P = [(100 * S.I)/(R * T)] = [(100 * 2000)/(5 * 8)] = 5000

[C.I. - S.I.] for 4 years may be calculated.
In this case, III is redundant.

I and III give us R and P, using
P{[1 + (5/100)]^2 - 1} - [(P * 5 * 2)/100] = 12.50
So, [C.I. - S.I.] for 4 years may be calculated.

69.
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? [Bamk P.O. 1999]

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.
Answer: d) I or III only

Solution:   I gives Rate = 5% p.a.
II gives, S.I. for 1 year = Rs. 600
III gives, sum = 10 * (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 * 2) = Rs. 1200

Now, from III, Sum = Rs. (10 * 1200) = Rs. 12000
Thus, Rate = [(100 * 1200)/(2 * 12000)] = 5%.

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

Hence, I or III is redundant.
70.
What is the total compound interest earned at the end of 3 years? [S.B.I.P.O. 2003]

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
Answer: d) Either II or III only

Solution:   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 * 4500)/(10 * 3)] = 15000.
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