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

In what time will Rs. 8,000 at 3% simple interest per annum produce the same amount as Rs.6,000 does in 5 years at 4% simple interest ? रू. 8,000 पर कितने समय में 3% साधारण ब्याज प्रति वर्ष की दर से उतना ही मिश्रधन प्राप्त होगा जितना कि रू. 6,000 पर 4% प्रति वर्ष साधारण ब्याज की दर पर 5 वर्ष में प्राप्त होता है?

  1. 3 years/वर्ष

  2. 4 years/वर्ष

  3. 5 years/वर्ष

  4. 6 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Rs. 6000 at 4% for 5 years: SI = 6000 × 0.04 × 5 = Rs. 1200. Amount = 7200. For Rs. 8000 at 3%, we need same interest. 8000 × 0.03 × T = 1200. T = 1200/(240) = 5 years. Set the interest amounts equal and solve for time.

Multiple choice

A sum of money lent out at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is

  1. Rs.500

  2. Rs.600

  3. Rs.700

  4. Rs.710
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After 2 years, amount = 720. After further 5 years (total 7 years), amount = 1020. So interest for 5 years = 1020 - 720 = 300. Interest per year = 60. Interest for 2 years = 120. Principal = Amount after 2 years - Interest for 2 years = 720 - 120 = 600. Option B is correct.

Multiple choice

Amount invested by Alok double itself in 5 years at compound interest. Alok earn 3900 as interest in 10 years. If Alok doubles his investment after 5 years, then find the compound interest now Alok will receive at the end of 10 years?

  1. 9100

  2. 7800

  3. 5200

  4. 4200

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

The question is ambiguous - 'doubles his investment after 5 years' could mean reinvesting the accumulated amount or adding an equal principal. Without clarity on the compounding mechanism, a definitive answer cannot be calculated.

Multiple choice

Ramesh gave two different sum at simple interest of 15% and 8% for 4 years and 5 years to Atul and Aakash respectively. If he received Rs 1280 and Rs 1008 from them, then find the ratio of the sum lend to Aakash and Atul by Ramesh.

  1. 10 : 9

  2. 9 : 8

  3. 9 : 10

  4. 8 : 9

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

For Atul: P1 × 15 × 4 / 100 = 1280, so P1 = Rs. 2133.33. For Aakash: P2 × 8 × 5 / 100 = 1008, so P2 = Rs. 2520. Ratio Aakash:Atul = 2520:2133.33 = 9:7.99 ≈ 9:8 after rounding.

Multiple choice

Anurag invests Rs. 9525 in a bond at a compound annual interest rate which gives interest at 3% per annum during the first year, 5% during the second year and 8% during the third year. How much amount does he get at the end of the third year.

  1. Rs. 11125.40

  2. Rs. 11050.60

  3. Rs. 12060.50

  4. Rs. 13025.40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For compound interest with varying rates: Amount = Principal × (1 + r1/100) × (1 + r2/100) × (1 + r3/100). Amount = 9525 × (1.03) × (1.05) × (1.08) = 9525 × 1.03 × 1.05 × 1.08 = 9525 × 1.168... = Rs. 11125.40 (approximately).

Multiple choice

The compound interest on a certain sum for 2 years is Rs. 410 and simple interest is Rs. 400. The rate of interest per annum is - किसी धनराशि पर 2 वर्ष का चक्रवृद्धि ब्याज 410 रू. और साधारण ब्याज 400 रू. है, तो प्रति वर्ष ब्याज की दर है-

  1. 10%

  2. 8%

  3. 5%

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

For 2 years, the difference between CI and SI is P(r/100)² = 410-400=10. From SI: 2Pr/100=400, so Pr/100=200. Therefore (r/100)×200=10, giving r/100=1/20, hence r=5%. The 5% rate satisfies both conditions.

Multiple choice

In a scheme a sum gives 50% of sum as compund interest. A man invested three amount for 5 years, 10 years and 15 years respectively. Find the ratio between the amount he invested if at the end he recieve same amount from all the investment?

  1. 9 : 6 : 4

  2. 9 : 8 : 7

  3. 9 : 6 : 5

  4. 9 : 8 : 2

  5. 9 : 3 : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using CI formula A = P(1 + r)^t where r = 50% = 1/2. For equal final amounts: P1 × (3/2)^5 = P2 × (3/2)^10 = P3 × (3/2)^15. Taking ratios: P1 : P2 : P3 = (3/2)^-5 : (3/2)^-10 : (3/2)^-15. Inverting and simplifying: P1 : P2 : P3 = 2^15/3^5 : 2^20/3^10 : 2^25/3^15. Common ratio gives 9 : 6 : 4. Work backwards from equal final amounts.

Multiple choice

Pawan invests half his capital at the rate of 10% per annum, one third at 9% and the rest at 12% per annum. Find the average rate of interest per annum, which he gets. पवन अपनी पूँजी का आधा 10% वार्षिक ब्याज की दर से, एक तिहाई को 9% ब्याज की दर से और शेष को 12% ब्याज की दर से निवेश करता है। औसत ब्याज की दर ज्ञात कीजिये जो वह प्राप्त करता है।

  1. 9%

  2. 10%

  3. 10.5%

  4. 12%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total capital be Rs. x. Half at 10% gives (x/2) × 10% = 5x%. One-third at 9% gives (x/3) × 9% = 3x%. Remaining (x - x/2 - x/3) = x/6 at 12% gives (x/6) × 12% = 2x%. Total interest = 5x% + 3x% + 2x% = 10x%. Average rate = 10x%/x = 10%.

Multiple choice

The amount on Rs.25000 in 2 years at annual compounded interest, if the rates for the successive years be 4% and 5% per annum respectively is- रु.25000 का 2 वर्षों में मिश्रधन क्या है जब क्रमिक वर्षों के लिए ब्याज दरें क्रमशः 4% और 5% है-

  1. Rs./रु.30000

  2. Rs./रु.26800

  3. Rs./रु.27300

  4. Rs./रु.28500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For first year at 4%: 25000 × 1.04 = Rs. 26000. For second year at 5%: 26000 × 1.05 = Rs. 27300. Alternatively, using the formula A = P(1 + r1)(1 + r2) = 25000 × 1.04 × 1.05 = 25000 × 1.092 = Rs. 27300.

Multiple choice

The compound interest earned by Monali on a certain amount at the end of two years at the rate of 8 p.c.p.a. was Rs. 1414.4. What was the total amount that Monali got back at the end of two years? एक निश्चित धनराशि पर दो वर्ष के अन्त में 8% वार्षिक ब्याज की दर से मोनाली को प्राप्त चक्रवृद्धि ब्याज रू. 1414.4 था। 2 वर्ष के अन्त में मोनाली को प्राप्त होने वाला कुल मिश्रधन क्या था?

  1. Rs. 8500

  2. Rs. 9414.4

  3. Rs. 8914.4

  4. Rs. 9914.4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound interest for 2 years at 8%: CI = P[(1 + 8/100)^2 - 1] = P[1.1664 - 1] = 0.1664P. Given CI = Rs. 1414.4, so P = 1414.4/0.1664 = Rs. 8500. Total amount = P + CI = 8500 + 1414.4 = Rs. 9914.4.

Multiple choice

The simple interest accrued on an amount of Rs.14800 at the end of three years is Rs.6216. What would be the compound interest accrued on the same amount at the same rate in the same period? एक धनराशि रु.14800 पर प्राप्त किया गया तीन वर्षों के अंत में साधारण ब्याज रु.6216 है | उसी राशि पर समान समय के लिए समान ब्याज दर से कितना चक्रवृद्धि ब्याज प्राप्त होगा ?

  1. Rs./रु.6986.1142

  2. Rs./रु.7042.2014

  3. Rs./रु.7126.8512

  4. Rs./रु.8321.4166
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest: 6216 = 14800 × R × 3, so Rate R = 6216/(14800×3) = 14% per annum. Compound Interest for 3 years at 14%: 14800 × [(1.14)^3 - 1] = 14800 × (1.481544 - 1) = 14800 × 0.481544 = Rs.7126.85. The difference between compound and simple interest arises because CI earns interest on interest, while SI only earns on the principal. For the same rate and period, CI is always greater than SI when time > 1 year.

Multiple choice

Simple interest on a certain sum at a certain annual rate of interest is 16% of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is एक निश्चित धनराशि पर किसी निश्चित ब्याज की वार्षिक दर पर साधारण ब्याज राशि का 16% है । यदि दर प्रतिशत और वर्षों में समय को प्रदर्शित करने वाली संख्या राशियाँ बराबर हैं, तो ब्याज दर है

  1. 4%

  2. 6%

  3. 4.5%

  4. 6.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let rate = R% and time = T years. Given rate = time, so R = T. Simple Interest = Principal × R × T / 100 = P × R × R / 100. Also given: SI = 16% of Principal = 0.16P. So P × R² / 100 = 0.16P, giving R² = 16. Therefore R = 4% (rate cannot be negative). Verification: 4% rate for 4 years gives SI = P × 4 × 4 / 100 = 16% of P.

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 एक निश्चित मूलधन पर x% चक्रवृद्धि वार्षिक ब्याज की दर से द्वितीय वर्ष का चक्रवृद्धि ब्याज प्रथम वर्ष के चक्रवृद्धि ब्याज से 110% अधिक है | द्वितीय वर्ष के चक्रवृद्धि ब्याज और पांचवे वर्ष के साधारण ब्याज में अन्तर रु.12 है | मूलधन है

  1. Rs./रु.1250

  2. Rs./रु1000

  3. Rs./रु1200

  4. Rs./रु1320
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For compound interest, interest in year n = P(1+r/100)^(n-1) × r/100. CI for 2nd year is 110% of 1st year means (1+r/100) = 2.1, so r = 110%. CI for 2nd year = P × 1.1 × 1.1 = 1.21P. SI for 5th year = P × 5 × 1.1 = 5.5P. Difference = 5.5P - 1.21P = 12. P = 1200.

Multiple choice

The difference in simple interest and compound interest for two years is Rs,144 at the rate of 20% per annum.Then what is the amount?

  1. Rs.3000

  2. Rs.3600

  3. Rs.4500

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

The difference between CI and SI for 2 years is CI - SI = P(r/100)² where P is principal. Given: 144 = P(20/100)² = P(0.04), so P = 144/0.04 = Rs.3600. The amount asked for is Rs.3600. Verification: SI for 2 years at 20% = Rs.1440, CI = 3600(1.2)² - 3600 = Rs.1584, difference = Rs.144.