Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

Ravi invests an amount of Rs. y in Scheme X, which offers compound interest at a rate of q% per annum, compounded annually, for n years. At the same time, he deposits an identical amount in Scheme Y, which provides compound interest at s% per annum, compounded half-yearly, for n years. If the total interest earned from both schemes is the same, which of the following pairs of q and s (both integers) satisfy this condition? (i) 14, 18 (ii) 96, 80 (iii) 36, 32 (iv) 69, 60 (v) 25, 30

  1. Only (i) and (ii)

  2. Only (iii) and (iv)

  3. Only (ii) and (iv)

  4. Only (ii) and (iii)

  5. Only (i), (ii), and (v)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total interest is the same if the effective annual rates are equal. For Scheme X, rate is q. For Scheme Y, rate is s compounded half-yearly, effective rate is (1 + s/200)^2 - 1. Testing (ii) 96% and 80%: (1 + 0.96) = 1.96; (1 + 0.8/2)^2 = 1.4^2 = 1.96. Testing (iv) 69% and 60%: (1 + 0.69) = 1.69; (1 + 0.6/2)^2 = 1.3^2 = 1.69.

Multiple choice

Directions: The question below is followed by two statements A and B. You are to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answer What is the rate of interest p.c.p.a. on an amount of Rs. 15,000 deposited in a Bank? (A) The simple interest for three years is Rs. 2,700. (B) The difference between the simple interest and compound interest is Rs. 165.24.

  1. If statement (A) alone is sufficient to answer the question, but statement (B) alone is not sufficient.

  2. If statement (B) alone is sufficient to answer the question, but statement (A) alone is not sufficient.

  3. If both statements (A) and (B) together are needed to answer the question.

  4. If either statement (A) alone or statement (B) alone is sufficient to answer the question.

  5. if you cannot get the answer from the statement A and B together, but need even more data.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: The question below is followed by two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. What is the per cent rate of simple interest per annum? I. The amount doubles in 6 years with the interest rate. II. The interest amount is Rs. 16,00 for the first year.

  1. Data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. Data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. Data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. Data given in both the statements I and II together is not sufficient to answer the question.

  5. Data in both the statements I and II together is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: Amount doubles in 6 years (A=2P). Simple interest formula: I = P*r*t/100. P = P*r*6/100 => 1 = 6r/100 => r = 100/6 = 16.67%. This is sufficient. Statement II: Interest for 1st year is 1600. Without the principal, we cannot find the rate. Thus, I alone is sufficient.

Multiple choice

A bank offers an annual interest rate of r% for 3 years. Using annual compounding, the compound interest (CI) is P [ ( 1 + r 100 ) 3 − 1 ] , and the simple interest (SI) is 3 P r 100 . For the same principal P and rate r, by what percentage is CI greater than SI? (1) r = 8 (2) P = $50,000

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CI - SI = P * (1 + r/100)^3 - P - 3Pr/100. The percentage difference is (CI - SI)/SI. This expression depends only on r. Statement (1) gives r, so it is sufficient. Statement (2) gives P, which cancels out in the percentage calculation, so it is not sufficient.

Multiple choice

Emily and Michael each invested in a bond that pays simple interest at an annual rate of 8% for one year. How many more dollars did Emily invest than Michael? (1) In one year, Emily earned \$18 more in interest than Michael. (2) If the annual simple interest rate had been 12%, Emily would have earned \$27 more in interest than Michael in one year.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let E and M be the investments. Interest = P * r * t. (1) 0.08E - 0.08M = 18 => E - M = 18/0.08 = 225. (2) 0.12E - 0.12M = 27 => E - M = 27/0.12 = 225. Both statements independently provide the difference E - M.

Multiple choice

At the start of the academic year, two students planned their savings for a skill-development course. Neha chose a long-term deposit option, while Arjun chose a mixed plan that combined a shorter deposit with a one-year simple-interest reinvestment. Neha deposits Rs. 1,12,000 in a scheme for 4 years at 6% interest per annum, compounded half-yearly. Separately, Arjun deposits a certain amount in the same scheme for 3 years, and then reinvests the entire amount he receives at the end of 3 years for 1 year at 12% simple interest. If the amounts received by both at the end of 4 years are equal, then the initial investment, in rupees, made by Arjun is ______.

  1. Rs. 1,06,090

  2. Rs. 1,06,900

  3. Rs. 1,04,090

  4. Rs. 96,090
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: Given below is a question followed by three statements I, II and III. Read the question and the statements carefully and choose your answer according to the set of statement(s) which is/are sufficient to answer the question. What is the principal amount? I. The sum becomes double in 10 years at 10% per annum simple interest. II. The compound interest obtained on the principal is 1830.4 after two years at the rate of 8% compounded annually. III. The simple interest obtained on the principal after 2 years at 8% rate of interest is 70.4 less than the compound interest obtain on the same principal after 2 years at 8% per annum.

  1. Only II

  2. Only III

  3. Either I or II

  4. Either II or III

  5. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement II provides enough info to find the principal using the compound interest formula for 2 years. Statement III provides the difference between CI and SI for 2 years, which is also sufficient to find the principal using the formula P(r/100)^2. Statement I is also sufficient.

Multiple choice

To start a new enterprise, Mr. Yogesh had borrowed a total of Rs. 60,000 from two moneylenders with the interest being compounded annually to be repaid at the end of two years. Mr. Yogesh repaid Rs. 38,800 more to the first moneylender compared to the second moneylender at the end of two years. The first moneylender charged an interest rate, which was 10% more than what was charged by the second moneylender. If Mr. Yogesh had instead borrowed Rs. 30,000 from each at their respective initial rates for two years, then he would have paid Rs. 7500 more to the first moneylender as compared to the second. The money borrowed by Mr. Yogesh from the first moneylender is (approx.)

  1. Rs. 20,000

  2. Rs. 35,000

  3. Rs. 40,000

  4. Rs. 42,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a complex system of equations involving compound interest. Given the constraints and the provided answer, 40,000 is the consistent solution.

Multiple choice

How much money did Yami borrow?Statement I: If borrowed for 6 years at 6% rate of interest per annum, she has to give double interest as earlier. Statement II: If the rate of interest per annum increases from 6% to 8% then she could borrow 25% less to give same amount of interest.A) If the data in statement I alone is sufficient to answer the question.

  1. A

  2. B

  3. C

  4. D

  5. E
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: I = P*R*T/100. Double interest means 2I = P*6*6/100. This is one equation with two variables (P and I). Statement II: 0.06*P*T = 0.08*(0.75P)*T. This is a tautology (0.06 = 0.06) and does not help find P. Both together are insufficient.

Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Karamjeet invested Rs. 60,000 in schemes A and Rs. 40,000 in scheme B at simple interest. What is his overall profit? I. The rate of interest in both the schemes is same, i.e. 4%, and the profit earned from scheme A is Rs. 4000. II. Time for which money was invested in scheme B is twice the time for which money was invested in scheme A.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the rate and profit for A, allowing us to find the time for A. Statement II gives the relationship between the times for A and B. We need both to calculate the profit for B and thus the overall profit.

Multiple choice

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities.

Quantity I: If a sum of money at simple interest amounts to Rs. 750 in 3 years and to Rs. 762 in 4 years, then the sum is: Quantity II: If a sum of money at simple interest amounts to Rs. 740 in 2 years and to Rs. 760 in 3 years, then the sum is:

  1. Quantity II > Quantity I

  2. Quantity II ≥ Quantity I

  3. Quantity II < Quantity I

  4. Quantity Il ≤ Quantity I

  5. Quantity Il = Quantity I, or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Quantity I, the interest for 1 year is Rs. 762 - Rs. 750 = Rs. 12, so the principal is Rs. 750 - (3 * 12) = Rs. 714. For Quantity II, the interest for 1 year is Rs. 760 - Rs. 740 = Rs. 20, so the principal is Rs. 740 - (2 * 20) = Rs. 700. Comparing the two, Quantity II (700) is less than Quantity I (714).

Multiple choice

Passage

Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

What is the rate of interest per annum? I. The compound interest in 5 years is more than the amount. II. The difference between simple interest and compound interest for 3 years is Rs. 540. III. An amount double itself simple interest in 5 years.

  1. Only I and II

  2. Only III

  3. Either I and II or III

  4. None of the three statements

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III says an amount doubles in 5 years at simple interest. SI = P*R*T/100. P = P*R*5/100, so R = 20%. This is sufficient to determine the rate.

Multiple choice

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both of these quantities.

Quantity I: The present worth of Rs. 132 due in 2 years at 5% simple interest per year. Quantity II: The present worth of Rs. 260 due in 2 years at 2% simple interest per year.

  1. Quantity I ≤ Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I > Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. Mark your answer as per these codes: (a) (A) and (B) together are sufficient. (b) Only (B) is sufficient. (c) Any of the three is sufficient. (d) Only (C) is sufficient. (e) All are necessary to answer the given question.

Shivani deposited a sum of money on simple interest at 10% rate of interest for 4 years and also deposited the same sum of money on compound interest for two years. At what rate did she deposit the money on compound interest? (A) Shivani got 4000 as simple interest on money she deposited after one year. (B) The sum of money she deposited amounted to Rs. 44,100 in 2 years compounded annually. (C) The rate of interest on compound interest was less than the rate of interest on simple interest.

  1. a

  2. b

  3. c

  4. d

  5. e
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the compound interest rate, we need the principal and the amount. Statement (B) provides the amount after 2 years. Statement (A) provides the simple interest for one year, which allows us to find the principal (since SI = P*r*t/100, 4000 = P*0.10*1). With P and the amount after 2 years, we can calculate the compound interest rate. Statement (C) is supplementary.

Multiple choice

Passage

Directions: Study the following information carefully and answer the question that follows. Three partners, Kiran, Priya, and Raman, invested some money to start up two small-scale industries, S1 and S2. Kiran invested Rs. 60,000 for 7 years in S1, while Raman invested Rs. 10,000 more than what Kiran invested in S1, but he invested for just 5 years. Priya did not invest anything in S1. Kiran invested in S2 double the amount invested by Priya in S2. Raman invested Rs. 20,000 for 6 years in S2. The amount invested by Priya in S2 is double the amount invested by Raman in S2. However, Priya invested for 2 years, and Kiran invested for 4 years in S2. The total profit earned from S1 is Rs. 3,30,000, while the total profit earned from S2 is Rs. 5,20,000. The total profit earned from S1 is Rs. 3,30,000, while the total profit earned from S2 is Rs. 5,20,000.

If Raman deposits the amount earned by him in S1 for 3 years at 8% rate of interest in the bank while Priya deposits the amount earned by her in S2 at 5% rate of interest for 2 years, then what would be the sum of the simple interest gained by both of them from the bank?

  1. Rs. 40,000

  2. Rs. 42,000

  3. Rs. 44,000

  4. Rs. 46,000

  5. Rs. 48,000
Reveal answer Fill a bubble to check yourself
C Correct answer