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

How much simple interest will earn on Rs. 5600 in 15 months at 12.5% per annum? / रु 5600, 15 महीने मेंप्रति वर्ष 12.5% की दर से साधारण ब्याज कितना होगा?

  1. 1500

  2. 750

  3. 650

  4. 875
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SI = (P × R × T) / 100 = (5600 × 12.5 × 1.25) / 100 = 5600 × 0.125 × 1.25 = 700 × 1.25 = 875. Note that 15 months = 1.25 years, not 1.15 years. Option A (1500) would result from incorrectly using 15 years instead of 1.25 years.

Multiple choice

At a certain rate of interest sum become 8 times itself in 14 years. In how many years will it become 16 times itself? एक निश्चित साधारण ब्याज की दर से एक धनराशि 14 वर्षों में स्वयं की 8 गुनी हो जाती है। कितने वर्षों में यह राशि खुद की 16 गुनी हो जायेगी?

  1. 24.75

  2. 28

  3. 30

  4. 32.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let principal be P and rate be r%. In simple interest, amount = P(1 + rt/100). In 14 years, amount = 8P, so P(1 + 14r/100) = 8P. This gives 14r/100 = 7, so r = 50%. To become 16 times: P(1 + 50t/100) = 16P, so t/2 = 15, giving t = 30 years.

Multiple choice

A man deposited two equal amount in a bank at the same rate of interest. If the difference between CI and SI for 4 years is Rs.434 more than difference between CI and SI for 3 years and rate of interest is 12.5% p.a. Then find each amount deposited by him ?

  1. Rs.8000

  2. Rs.7850

  3. Rs.8192

  4. Rs.10000

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

The difference between CI and SI for n years is P[(1 + r/100)^n - 1 - nr/100]. For n=3 at 12.5%, this is P[(1.125)^3 - 1 - 0.375] = P[0.0488]. For n=4, it is P[(1.125)^4 - 1 - 0.5] = P[0.1018]. The difference is P[0.052979] = 434, so P = 8192.

Multiple choice

The simple interest on a certain sum for 2 years at a certain rate of interest is Rs.2000 and compound interest on the same sum, same time and same rate of interest is Rs.2050. Then find the ratio between CI for 2 years and SI for 3 years?

  1. 60:41

  2. 41:60

  3. 51:60

  4. 60:51

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

SI for 2 years = 2000, so SI for 1 year = 1000. This means interest = 1000 annually. Principal P such that P × R × 2/100 = 2000. CI for 2 years is given as 2050. Using the CI formula and solving, we get CI for 2 years = 2050 and SI for 3 years = 3000. The ratio is 2050:3000 = 41:60.

Multiple choice

A certain amount of money is lent out at compound interest at the rate of 20% per annum for two years, compounded annually. It would give Rs. 482 more if the amount is compounded half yearly. Find the principle.

  1. 18000

  2. 17500

  3. 20000

  4. 24700

  5. 25600
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Annual compounding: Amount = P(1.2)² = 1.44P. Half-yearly: Rate = 10% per half-year, Amount = P(1.1)⁴ = 1.4641P. Difference = P(1.4641 - 1.44) = 0.0241P = 482. Therefore P = 482/0.0241 ≈ 20000. The key insight is that more frequent compounding yields higher returns.

Multiple choice

Find the rate of interest. I. A sum of money becomes double of itself at simple interest in 12.5 years. II. 5000 becomes 5832 in 2 years at compound interest.

  1. Only I

  2. Only II

  3. Both I and II

  4. Either I or II

  5. Neither I nor II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: Sum doubles in 12.5 years at simple interest, so rate = 100/12.5 = 8% per annum. Statement II: 5000 becomes 5832 in 2 years at CI. Using formula 5832 = 5000(1 + r/100)², we get r = 8% per annum. Either statement alone gives rate = 8%.

Multiple choice

If the compound interest on a certain sum for 2 yeas is Rs. 70. 70 and the simple interest is Rs. 70, then the rate of interest per annum is-

  1. 7%

  2. 3%

  3. 5%

  4. 2%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the principal and r be the rate percent. SI for 2 years = P × r × 2/100 = 70, so Pr/50 = 70. CI for 2 years = P(1 + r/100)² - P = 70.70. Expanding: P(1 + 2r/100 + r²/10000) - P = 70.70, so 2Pr/100 + Pr²/10000 = 70.70. Substituting Pr = 3500: 2(3500)/100 + 3500r/10000 = 70.70, giving 70 + 0.35r = 70.70, so 0.35r = 0.70 and r = 2%.

Multiple choice

Find the compound interest on Rs.25000 in 2 years at the rate of 12% compounded annually. 25000 रु. की धनराशि पर 12% चक्रवृद्धि ब्याज की दर से 2 वर्ष का चक्रवृद्धि ब्याज ज्ञात कीजिये ।

  1. Rs.6120

  2. Rs.6240

  3. Rs.6210

  4. Rs.6360
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the compound interest formula A = P(1 + r/100)^n: For P=25000, r=12%, n=2 years. Year 1: 25000 × 1.12 = 28000. Year 2: 28000 × 1.12 = 31360. Compound Interest = 31360 - 25000 = 6360. This can also be calculated directly: CI = P[(1 + r/100)^n - 1] = 25000[(1.12)^2 - 1] = 25000(1.2544 - 1) = 25000 × 0.2544 = 6360.

Multiple choice

What is difference of the compound interest earn on Rs.15000 at the rate of 16% for 2 year and 3 year ? 2 साल और 3 साल के लिए 16% की दर से 15000 रुपए पर चक्रवृद्धि ब्याज का क्या अंतर है?

  1. 3400

  2. 3200

  3. 3300

  4. 3000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Compound interest for 3 years minus compound interest for 2 years gives the interest earned in year 3 only. For 16% rate, amount after 2 years = P(1.16)², after 3 years = P(1.16)³. The difference is P(1.16)³ - P(1.16)² = P(1.16)²(0.16) = 15000 × 1.3456 × 0.16 = 3200 rupees approximately. Alternatively, this is the simple interest on the amount after 2 years for one more year at 16%.

Multiple choice

The compound interest on a certain sum for 2 years is Rs. 4100 and the simple interest is Rs. 4000. Then the rate of interest is-

  1. 4%

  2. 5%

  3. 6%

  4. 8%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between compound interest and simple interest for 2 years is the interest on the first year's interest. CI - SI = Rs. 4100 - Rs. 4000 = Rs. 100. This Rs. 100 is the interest on the first year's simple interest. So if first year SI = Rs. 2000 (half of Rs. 4000), then Rs. 100 is interest on Rs. 2000 for 1 year. Therefore Rate = (100/2000) × 100 = 5%.

Multiple choice

Sangram invests certain sum for 2 years in scheme P offering compound interest of 20% per annum. He also invests less than previous by Rs. 1600 in scheme Q for 3 years offering simple interest at 10% per annum. The interest received from scheme P was twice the interest received from scheme Q. what is the sum of money invested by Sangram in scheme Q?

  1. 3400

  2. 4400

  3. 3000

  4. 2000

  5. 6000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P's investment be x. CI for 2 years at 20% = x×(1.2²-1) = x×0.44 = 0.44x. Q's investment is x-1600. SI for 3 years at 10% = (x-1600)×0.3. Given: 0.44x = 2×0.3×(x-1600), so 0.44x = 0.6x - 960. Solving: 0.16x = 960, x = 6000. Q's investment = 6000-1600 = 4400. Option B is correct. Common mistake: using wrong CI formula or misinterpreting the relationship.

Multiple choice

A man has two sons whose ages are 15 years and 13 years. The man has 4,50,000 rupees . He gives some money to his elder son and remaining to the younger son. If bank gives 5% interest to the elder son and 2% interest to the younger son and after completing 18 years of their ages the bank gives same money to both the sons then find what amount of money ( in rupees ) the man gave to his both sons.

  1. 3,25,000 , 1,25,000

  2. 2,00,000 , 2,50,000

  3. 1,50,000 , 3,00,000

  4. 2,20,000 , 2,30,000

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

Let elder son get x, younger get (450000-x). After interest: x(1+0.05×3) and (450000-x)(1+0.02×5) must be equal. Solving: 1.15x = 1.1(450000-x) → 2.25x = 495000 → x = 220000. Elder gets 2,20,000; younger gets 2,30,000. Option D is correct.

Multiple choice

On a certain principal the compound interest compounded annually for the second year at (x)% per annum is 110% of the compound interest for the first year. The difference in the compound interest for the second year and simple interest for the fifth year on the same principal is Rs.12. The principal is-

  1. Rs. 1800

  2. Rs. 1500

  3. Rs. 1250

  4. Rs. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let principal = P, rate = x%. CI for 1st year = P × x/100. CI for 2nd year = P(1 + x/100) × x/100 = (P × x/100)(1 + x/100). Given: 2nd year CI is 110% of 1st year CI, so (1 + x/100) = 1.10, giving x = 10%. SI for 5 years = P × 10 × 5/100 = P/2. CI for 5 years = P(1.1^5 - 1) ≈ 0.61051P. Difference = 0.61051P - 0.5P = 0.11051P ≈ Rs. 12. So P ≈ Rs. 108.6. Wait, let me reconsider. The difference between CI for 2nd year and SI for 5th year: CI(2nd year) = P × 0.1 × 1.1 = 0.11P. SI for 5th year alone = P × 0.1 = 0.1P. Difference = 0.11P - 0.1P = 0.01P = 12. So P = Rs. 1200.

Multiple choice

The simple interest on a certain sum for 8 months at 4% per annum is Rs.129 less than the simple interest on the same sum for 15 months at 5% per annum. What is the sum?

  1. Rs.2580

  2. Rs.2400

  3. Rs.2529

  4. Rs.3600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the sum. SI1 = P × 4 × 8/12 × 100 = P × 32/1200. SI2 = P × 5 × 15/12 × 100 = P × 75/1200. Given SI2 - SI1 = 129, so P × (75-32)/1200 = 129, P × 43/1200 = 129, P = 129 × 1200/43 = 3600. The difference in interest rates and time periods must be carefully accounted for.

Multiple choice

The following questions are accompanied by two statements I and II. You have to determine which statement/statements is/are sufficient to answer the question. Mark your answer - A certain sum of money doubles itself at simple interest in 5 years. How much is the principal amount? I. The rate of interest is 20 percent per annum. II. The sum would triple itself in 10 years.

  1. If only statement I is sufficient.

  2. If only statement II is sufficient.

  3. If either I or II is sufficient.

  4. If neither I nor II is sufficient.

  5. If both statements I and II are necessary.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From the problem: P doubles in 5 years at simple interest. So 2P = P(1 + 5r), giving r = 20%. Statement I gives the same rate (20%). Statement II: 3P = P(1 + 10r) gives r = 20%. Both statements give the same information but NO principal amount can be determined since the relationship works for ANY principal P. Therefore neither statement alone is sufficient to find the principal value.