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

Directions: Compare the two quantities in A and B. | Quantity A | Quantity B | | --- | --- | | Simple interest on \$500 @ 10% for 2 years | Compound interest on \$400 @ 10% for 2 years |

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity A: SI = 500 * 0.10 * 2 = 100. Quantity B: CI = 400 * (1 + 0.10)^2 - 400 = 400 * 1.21 - 400 = 484 - 400 = 84. Since 100 > 84, Quantity A is greater.

Multiple choice

Ravi wants to invest Rs. 20,000 in a scheme for 3 years. At the end of 3 years, he is expected to receive Rs. 32,000. The current rate of interest available in the market for 3 years is 10% per annum compounded annually. Decide whether Ravi should go in for the investment or not. If he goes for the investment, what will be his loss/profit?

  1. No, Rs. 6,000 loss

  2. Yes, Rs. 5,380 profit

  3. No, Rs. 5,000 loss

  4. Yes, Rs. 7,000 profit
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Future value of 20,000 at 10% compound interest for 3 years is 20000 * (1.1)^3 = 20000 * 1.331 = 26,620. Ravi expects 32,000. Profit = 32,000 - 26,620 = 5,380.

Multiple choice

A person deposited Rs. 1000 in a bank at 5% compounded annually. After 5 years, the rate of interest was increased to 6% and after 4 more years, the rate was further increased to 7%. The money was withdrawn at the end of 12 years. Find the amount.

  1. Rs. 1973.88

  2. Rs. 1937.86

  3. Rs. 1930.59

  4. Rs. 1903.95

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

Amount = 1000 * (1.05)^5 * (1.06)^4 * (1.07)^3. Calculating this: 1000 * 1.27628 * 1.26247 * 1.22504 = 1973.88.

Multiple choice

Directions: Compare the two quantities in A and B. A family made a down payment of \$75 and borrowed the balance on a set of encyclopedias that cost \$400. The balance with interest was paid in 23 monthly payments of \$16 each and a final payment of \$9. | Quantity A | Quantity B | | --- | --- | | Amount of interest paid as a percent of the amount borrowed | 15% |

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cost = 400, Down payment = 75, Amount borrowed = 325. Total paid = (23 * 16) + 9 = 368 + 9 = 377. Interest paid = 377 - 325 = 52. Interest percent = (52 / 325) * 100 = 16%. Since 16% > 15%, Quantity A is greater.

Multiple choice

Directions: The question below is followed by two statements I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and choose the correct alternative. What is the rate of simple interest per annum? I. The amount doubles itself in 10 years with simple interest. II. The simple interest incurred in 5 years is Rs. 5000.

  1. The 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. The 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. The data in either statement I alone or statement II alone is sufficient to answer the question.

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

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

Statement I: Amount doubles in 10 years, so SI = P. P = (P*R*10)/100 -> R = 10%. Statement II: SI = 5000 in 5 years. Without the principal, R cannot be determined. Thus, I alone is sufficient.

Multiple choice

Directions: The problem contains a question and two statements giving certain data. You have to select the correct answer from the given options depending on the sufficiency of the data given in the statements to answer the question. At simple interest, what sum earns an interest of Rs. 5000 in 5 years? (A) The same sum earns an interest of Rs. 10,000 in 10 years. (B) The rate of interest is 5% p.a.

  1. Statement (A) alone is sufficient to answer the question and statement (B) alone is not sufficient to answer the question.

  2. Statement (B) alone is sufficient to answer the question and statement (A) alone is not sufficient to answer the question.

  3. Statements (A) and (B) together are sufficient to answer the question, but neither statement alone is sufficient.

  4. Each statement alone is sufficient to answer the question.

  5. Both statements (A) and (B) together are not sufficient to answer the question and additional data specific to the problem is needed.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest formula: SI = (P * R * T) / 100. We have SI=5000, T=5. 5000 = (P * R * 5) / 100 => P * R = 100,000. Statement (A) says 10000 = (P * R * 10) / 100 => P * R = 100,000 (redundant). Statement (B) says R = 5%. With R=5, P * 5 = 100,000 => P = 20,000. Thus, (B) is sufficient.

Multiple choice

Directions: In the following question, two quantities are given numbered I and II. Determine the relationship between the quantities and choose the appropriate option. Give answer according to these codes. Quantity I: Time in which the simple interest accrued on Rs. 2500 is less than the simple interest accrued on Rs. 2400 at 7% p.a. by Rs. 49 Quantity II: Time in which the simple interest accrued on Rs. 3000 is less than the simple interest accrued on Rs. 2500 at 5% p.a. by Rs. 100

  1. Quantity I ≤ Quantity II

  2. If Quantity I > Quantity II

  3. If Quantity I < Quantity II

  4. Quantity I ≥ Quantity II

  5. If Quantity I = Quantity II, or the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For Quantity I, the interest difference is 100 × 7% × t = 49, so t = 7 years. For Quantity II, the difference is 500 × 5% × t = 100, so t = 4 years. Hence Quantity I is greater than Quantity II.

Multiple choice

Directions: Study the following information carefully and answer the question. Amit and Rajat started an IT company in a partnership by investing Rs. 500000 and Rs. 200000, respectively. Rajat, who did all the financial work of the company, was supposed to get Rs. 5000 per month as his monthly wage. After receiving of 5% annual interest on the total capital, net profit was distributed between them according to their investment ratio. Total income earned in the first year of business was Rs. 200000. Later, Amit reinvested 60% his total amount received in the company for a period of 6 months and withdrew it afterwards. What will be the total amount received by Rajat for the second year, if it gave 30% annual return at the end of the second year?

  1. Rs. 33652

  2. Rs. 93652

  3. Rs. 103562

  4. Rs. 122500

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: In this problem, a question is followed by two statements labelled A and B. Read the statements carefully and decide which of the given statements is/are sufficient to answer the question. Choose the correct option accordingly. In how many years will a certain amount double itself at a simple interest? (A) The rate of interest is 5% p.a. (B) The principal amount is Rs. 20,000.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient.

  3. Both statements (A) and (B) together are sufficient, but neither of them alone is sufficient.

  4. Both statements (A) and (B) are sufficient independently.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest formula: SI = (P * R * T) / 100. To double, SI = P, so P = (P * R * T) / 100, which simplifies to 100 = R * T. If R is known (5%), T can be found. P is irrelevant as it cancels out.

Multiple choice

Directions: In this problem, a question is followed by two statements labelled A and B. Read the statements carefully and decide which of the given statements is/are sufficient to answer the question. Choose the correct option accordingly. In how many years will a certain amount 'a' increase by Rs. 205 at a rate of x% p.a. compound interest? (A) x = 5% (B) a is Rs. 205.

  1. Statement (A) alone is sufficient but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient but statement (A) alone is not sufficient.

  3. Both statements (A) and (B) together are sufficient but neither of them alone is sufficient.

  4. Both statements (A) and (B) are sufficient independently.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound interest formula: A = P(1 + r/100)^n. We need to find n. We have P = a, A = a + 205, r = x. Statement A gives r=5. Statement B gives P=205. Neither is sufficient alone because we have two variables (a and n) or need both P and r to solve for n.

Multiple choice

Directions: The question given below is followed by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the question. What is the sum of money? A. The difference between compound interest and simple interest on a certain sum of money for 2 years at 7% is Rs. 44.1. B. The compound interest for 2 years at 20% is Rs. 1800.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A: Difference between CI and SI for 2 years = P * (r/100)^2. With r=7, 44.1 = P * (0.07)^2, so P can be found. Statement B: CI = P * ((1 + r/100)^n - 1). With r=20, 1800 = P * ((1.2)^2 - 1), so P can be found. Both are sufficient independently.

Multiple choice

Directions: The following question is accompanied by statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. Find the amount received by Mr. Goyal at the end of 2 years, if the rate of interest is 12% compounded annually. (A) Mr. Goyal invested the same amount of money under simple interest at the rate of 15% per annum and received a total amount of Rs. 24,000 at the end of 4 years. (B) The difference between compound interest and simple interest on the same sum of money at 10% of interest at the end of 2 years is Rs. 150.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A allows us to find the principal (P) using SI = P*R*T/100, which is sufficient to calculate the compound interest amount. Statement B provides the difference between CI and SI for 2 years, which is P*(R/100)^2, allowing us to find P and subsequently the compound interest amount. Since both statements independently provide the necessary information to find the principal, either is sufficient.

Multiple choice

Directions: The question given below is followed by two statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. What is the rate of interest per annum? (A) The amount invested by a person is Rs. 10,000 and the difference between Compound interest and Simple Interest is Rs. 144 in two years. (B) The amount invest by the person is Rs. 10,000 and becomes Rs. 14,049.28 in three years at compound interest.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A allows calculating the rate using the formula for CI-SI difference for 2 years. Statement B allows calculating the rate using the compound interest formula for 3 years. Both are independently sufficient.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide 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 p.c.p.a. on an amount of Rs. 15,000 deposited in a bank? (1) The simple interest for two years is Rs. 3,600. (2) The difference between the simple interest and compound interest is Rs. 216.

  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 (1) and (2) 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