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

Rs 1500 is invested for 5 yr in scheme A which offers 14% p.a simple interest. The amount received with some extra money is invested in scheme B for 2ys compound interest(compounded annually) at the rate of 20% p.a. If the compound interest received from scheme B is Rs 1408 /-, what was the additional money invested in scheme B ?

  1. Rs.650

  2. Rs.450

  3. Rs.500

  4. Rs.750

  5. Rs.300
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Scheme A: Rs.1500 at 14% SI for 5 years. Amount = 1500 + (1500×0.14×5) = 1500 + 1050 = Rs.2550. Let additional money in Scheme B be x. Total in B = 2550 + x at 20% CI for 2 years. CI = (2550+x) × [(1.2)² - 1] = (2550+x) × 0.44 = 1408. Solving: 2550+x = 1408/0.44 = 3200, so x = Rs.650. First find SI amount, then use CI formula.

Multiple choice

The simple interest on a certain sum of money at a certain rate of interest after 2.5 years is Rs.150 and the compound interest on the same sum of money at the same rate after 2 years is Rs.126. Find the difference between the compound interest and the simple interest on the same sum of money at the same rate after 3 years.

  1. 20.25

  2. 18.6

  3. 26.25

  4. 20.50

  5. 16.50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let principal be P and rate be R%. SI for 2.5 years = P × R × 2.5 / 100 = 150, so PR = 150 × 100 / 2.5 = 6000. CI for 2 years at R% = P[(1 + R/100)² - 1] = 126. From PR = 6000, P = 6000/R. We need CI - SI after 3 years. CI₃ = P[(1 + R/100)³ - 1] and SI₃ = P × R × 3 / 100. The difference = P[(1 + R/100)³ - 1 - 3R/100]. Using CI₂ = P[(1 + R/100)² - 1] = 126 and solving gives R ≈ 6% and the difference ≈ 18.6. Option B is correct.

Multiple choice

What would be the approximate compound interest in 9 months of a sum of 1600 at the rate of interest 6% per annum when rate of interest is considered quarterly?

  1. Rs.73.2

  2. Rs.73.3

  3. Rs.73

  4. Rs.75

  5. Rs.77
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For quarterly compounding, the rate per quarter is 6%/4 = 1.5% and time is 9 months = 3 quarters. Using A = P(1 + r/100)^n, we get A = 1600 × (1.015)^3 ≈ 1673.09, so CI ≈ 73.09. Rounding to the nearest rupee gives Rs.73, which matches option C.

Multiple choice

An electric iron is sold for Rs. 440 cash or for Rs. 200 cash down payment together with Rs. 244 to be paid after one month. Find the rate of interest charged is the instalment scheme.

  1. 15%

  2. 20%

  3. 16.66%

  4. 25%

  5. 22.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cash price = Rs. 440. Installment total = Rs. 200 + Rs. 244 = Rs. 444. Extra amount (interest) = Rs. 4. This interest is charged on the amount not paid upfront = Rs. 440 - Rs. 200 = Rs. 240 for 1 month. Monthly rate = 4/240 = 1/60 ≈ 1.67%. Annual rate = 1.67% × 12 = 20%.

Multiple choice

On retirement Kamal gets Rs 3200000 as gratuity. He invested this amount in two banks in such a way that he earns Rs. 23000 every month as interest. If the annual interest rate of the banks are 9% and 8% respectively. What amount is invested in the bank with higher rate of interest?

  1. 120000

  2. 1200000

  3. 320000

  4. 200000

  5. 2000000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let x be the amount invested at 9%. Then (3200000-x) is invested at 8%. Annual interest from first bank: 0.09x. Annual interest from second bank: 0.08(3200000-x). Total annual interest: 23000×12 = 276000. So 0.09x + 0.08(3200000-x) = 276000. Solving: 0.09x + 256000 - 0.08x = 276000, so 0.01x = 20000, giving x = 2000000. This is the amount at 9% (higher rate), so the answer is correct.

Multiple choice

A sum of money placed at compund interest triples itself in 5 years. In what time will it amount to nine times itself ?

  1. 10 years

  2. 15 years

  3. 20 years

  4. 18 years

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

If money triples in 5 years at compound interest, the growth factor is 3^(1/5) per 5-year period. To reach 9 times (3^2), we need 2 periods of 5 years each, so 10 years. The pattern: 3 times in 5 years, 9 times in 10 years, 27 times in 15 years. This follows from (3)^(t/5) = 9, solving for t.

Multiple choice

The sum which amounts to Rs. 364.80 in 8 years at 3.5% simple interest per annum is- 8 वर्षों में 3.5% प्रतिवर्ष साधारण ब्याज की दर से जो रकम 364.80 रू. बन जाती है, वह राशि है-

  1. Rs. 285

  2. Rs. 280

  3. Rs. 275

  4. Rs. 270
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using simple interest formula: A = P(1 + rt). Given A = 364.80, r = 0.035, t = 8. So 364.80 = P(1 + 0.035 × 8) = P(1.28). Therefore P = 364.80 / 1.28 = 285. Verification: Interest = 285 × 0.035 × 8 = 79.80, Amount = 285 + 79.80 = 364.80.

Multiple choice

Two brothers received Rs 1200 each from their Father. First son lent the amount to his friend at compound interest and received Rs 1348.32 after 2 years. While the second son invested his sum at double the rate of interest at simple interest for 3 years. What is the difference of the amount received by both the brothers after their respective time period?

  1. 273.68

  2. 263.68

  3. 283.68

  4. 280.68

  5. 183.68
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First son: P=1200, A=1348.32, n=2 years. CI = A-P = 148.32. Using CI formula A=P(1+r/100)^n: 1348.32=1200(1+r/100)^2, so (1+r/100)^2 = 1.1236, giving 1+r/100 = 1.06, r = 6%. Second son: r = 12% (double), SI for 3 years = 1200 × 12 × 3/100 = 432. Amount = 1200 + 432 = 1632. Difference = 1632 - 1348.32 = 283.68.

Multiple choice

If the compound interest on certain sum of money in second year is Rs. 26.25, then find the compound interest after two years, when rate is given as 5% per annum ? यदि किसी निश्चित राशि का दूसरे वर्ष के लिए चक्रवृद्धि ब्याज 26.25 रू. हो तो दो वर्षं पश्चात् चक्रवृद्धि ब्याज ज्ञात कीजिए, जब ब्याज की दर 5% वार्षिक हो।

  1. Rs. 51.25

  2. Rs. 50.25

  3. Rs. 52.5

  4. Rs. 53.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the principal be P. CI for 2nd year = P × (1.05^2 - 1.05) = P × 0.0525 = 26.25. So P = 26.25 ÷ 0.0525 = 500. Total CI after 2 years = P × (1.05^2 - 1) = 500 × 0.1025 = Rs. 51.25. The compound interest for two years is Rs. 51.25.

Multiple choice

A sum of 6000 is divided between two brothers such that the simple interest on the amount for 2 years at 5% per annum for elder brother is equal to the simple interest on the amount for 3 years at 10% per annum for younger brother. Find the ratio between the interest occurred by elder and younger brother when compounded annually while keeping the remaining parameters same?

  1. 1 : 1

  2. 3 : 1

  3. 203 : 211

  4. 615 : 662

  5. Cannot be determined.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let elder brother get amount E and younger get amount Y, with E + Y = 6000. Simple interest equality: E × 5 × 2 = Y × 10 × 3, giving 10E = 30Y or E = 3Y. Substituting: 4Y = 6000, so Y = 1500, E = 4500. Compound interest for elder after 2 years at 5%: 4500(1.05)² - 4500 = 461.25. Compound interest for younger after 3 years at 10%: 1500(1.1)³ - 1500 = 496.5. Ratio = 461.25 : 496.5 = 615 : 662 after multiplying by 4/3.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? How much money did Prashant borrow from Arun? I. After 8 years Arun received Rs. 6,400 as simple interest from Prashant. II. Prashant invested 50% of the borrowed money somewhere and received Rs. 8,000 at that place. III. After 4 years the amount was 20% of the simple interest.

  1. Only I and II

  2. Only I and III

  3. All are necessary

  4. All together are not sufficient

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

We need to find the principal amount Prashant borrowed. Statement I: After 8 years, Arun received Rs. 6,400 as simple interest from Prashant. This gives SI = 6400, time = 8 years. But we don't know the rate or principal. Statement II: Prashant invested 50% of borrowed money and received Rs. 8,000 - we don't know the time, rate, or whether this is principal+interest. Statement III: After 4 years, amount was 20% of simple interest - this doesn't give us rate or principal. Even combining all statements, we have multiple unknowns (P, r) and cannot solve uniquely. The data is insufficient.

Multiple choice

Rs 15,000 is to be invested in 2 schemes, one part is invested in scheme A which offers 9.5% rate of interest and remaining part is invested in scheme B which offers 5% rate on interest. After 3 years, a total of Rs 3600 is received as simple interest. What is the part invested in scheme A?

  1. Rs. 10000

  2. Rs. 12000

  3. Rs. 15000

  4. Rs. 18000

  5. Rs. 20000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be invested in scheme A at 9.5% for 3 years. SI from A = 0.285x. SI from B (15000-x at 5% for 3 years) = 0.15(15000-x) = 2250-0.15x. Total: 0.285x + 2250 - 0.15x = 3600. Solving: 0.135x = 1350, x = 10000.