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

Ranbir deposits a certain sum in a bank. He gets 4% per annum interest for 3 years, 5% for next 2 years and 6% beyond that. If he gets Rs.2000 as simple interest for 8 years, how much money did he deposit in bank? राम एक निश्चित धनराशि को एक बैंक में जमा करता है | वह 3 वर्षों के लिए 4% वार्षिक ब्याज की दर से, अगले 2 वर्षों के लिए 5% वार्षिक ब्याज की दर से तथा उसके ऊपर 6% की दर से ब्याज प्राप्त करता है | यदि वह 8 वर्षों में कुल 2000 रु. प्राप्त करता है, उसने बैंक में कितनी धनराशि जमा की ?

  1. Rs./रु.3500

  2. Rs./रु.4000

  3. Rs./रु.4500

  4. Rs./रु.5000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total SI = P × 4/100 × 3 + P × 5/100 × 2 + P × 6/100 × 3 = 2000. Simplifying: P × 0.12 + P × 0.10 + P × 0.18 = 2000, so P × 0.40 = 2000, giving P = 2000/0.40 = 5000. Therefore, the deposited amount is Rs. 5000.

Multiple choice

The difference between compound interest and simple interest on certain sum at 10% per annum for 2 years is Rs.623. What is the sum? एक निश्चित धनराशि पर दो वर्षों में 10% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज और साधारण ब्याज में अन्तर 623 रु. है | राशि क्या है ?

  1. Rs./रु.62300

  2. Rs./रु.63100

  3. Rs./रु.64100

  4. Rs./रु.64400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 2 years at 10%, the difference between CI and SI is P(r/100)² where P is principal and r is rate. So 623 = P(10/100)² = P(0.01). Therefore P = 623/0.01 = 62300. This formula works because CI - SI for 2 years equals the interest on the first year's simple interest for one year.

Multiple choice

Ramesh borrowed a sum at 5 per annum simple interest from Rahul. He returns the amount after 5years. Rahul returns 2 % of the total amount received. How much did Ramesh borrowed if he received Rs. 5? रमेश एक धनराशि 5 प्रतिशत वार्षिक साधारण ब्याज की दर से राहुल से उधार लेता है | वह राशि को 5 वर्ष बाद लौटाता है | राहुल कुल प्राप्त राशि का 2 % लौटा देता है | रमेश ने कितना उधार लिया था यदि उसे 5 रु. प्राप्त हुए ?

  1. Rs.150

  2. Rs.175

  3. Rs.200

  4. Rs.250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rahul returns 2% of what he received, meaning he keeps 98%. Ramesh receives Rs. 5, which is 2% of the total amount Rahul got. So Rahul received 5/0.02 = Rs. 250. This is the amount after 5 years at 5% SI: P + P×5×5/100 = 250. So P + 0.25P = 250, meaning 1.25P = 250, so P = Rs. 200.

Multiple choice

The difference between compound interest and simple interest on a sum of Rs. 16000 at 5% per annum for 3 years is- 16000 रू. की धनराशि पर 5% वार्षिक ब्याज की दर से 3 वर्षों में साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर है-

  1. Rs. 112

  2. Rs. 118

  3. Rs. 132

  4. Rs. 122
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest = P×R×T/100 = 16000×5×3/100 = Rs. 2400. For Compound Interest, Amount = P(1+R/100)^T = 16000(1+5/100)³ = 16000×1.157625 = Rs. 18522, so CI = Rs. 2522. The difference = 2522 - 2400 = Rs. 122. Alternatively use direct formula: Difference for 3 years = PR²(300+R)/100³ = 16000×25×305/1000000 = Rs. 122.

Multiple choice

The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. What is the sum placed on simple interest? एक निश्चित धनराशि पर 8% प्रति वर्ष के हिसाब से 3 वर्ष का साधारण ब्याज 4000 रूपये पर 10% प्रति वर्ष के हिसाब से 2 वर्ष के चक्रवृद्धि ब्याज का आधा है। साधारण ब्याज पर रखी गयी धनराशि क्या है?

  1. Rs. 1550

  2. Rs. 1650

  3. Rs. 1750

  4. Rs. 2000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI on Rs. 4000 for 2 years at 10% = 4000[(1.1)² - 1] = 4000(1.21 - 1) = Rs. 840. SI = 840/2 = Rs. 420. For SI at 8% for 3 years: Principal × 8% × 3 = 420. Principal = 420/(0.24) = Rs. 1750.

Multiple choice

The compound interest on Rs.30000 at 7% per annum for a certain time is Rs.4347. Then the time is - 30000 रू. पर एक निश्चित समय के लिये 7% की दर से चक्रवृद्धि ब्याज 4347 रू. है तो समय है-

  1. 2 years/वर्ष

  2. 2.5 years/वर्ष

  3. 3 years/वर्ष

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

CI = P[(1+r/100)^t - 1], so 4347 = 30000[(1.07)^t - 1]. This gives (1.07)^t = 1 + 4347/30000 = 1.1449. Checking: 1.07² = 1.1449, therefore t=2 years.

Multiple choice

Out of a sum of Rs.625, a part was lent at 5% and the other at 10% simple interest. If the interest on the first part after 2 years is equal to the interest on the second part after 4 years then the second sum (in Rs.) is - रू 625 की धनराशि के एक भाग को 5% पर और दूसरे भाग को 10% साधारण ब्याज पर उधार लिया। पहले भाग का 2 वर्ष बाद ब्याज, दूसरे भाग पर 4 वर्ष बाद ब्याज के बराबर है। तो दूसरे भाग की धनराशि है - (रूपये में)

  1. 125

  2. 200

  3. 250

  4. 300
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let first part be x rupees, second part be (625-x). Simple interest equality: (x × 5 × 2)/100 = ((625-x) × 10 × 4)/100. Simplifying: 10x = 40(625-x), so x = 4(625-x), giving x = 2500-4x, so 5x = 2500, x = 500. Second part = 625-500 = Rs. 125.

Multiple choice

The compound interest on Rs.2000 for 3 years is Rs.315.25. The rate of interest is - रू 2000 पर 3 वर्ष के लिए चक्रवृद्धि ब्याज रू 315.25 है तो ब्याज दर है -

  1. 3%

  2. 4%

  3. 5%

  4. 6%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Testing the given options: At 5%, compound interest on Rs. 2000 for 3 years = 2000(1.05³ - 1) = 2000(1.157625 - 1) = 2000(0.157625) = Rs. 315.25. This matches exactly with the given compound interest.

Multiple choice

A sum of Rs.400 amounts to Rs.441 in 2 years. What will it amount to if the rate of interest is increased by 5%? एक 400 रू. की धनराशि 2 वर्षो में 441 रू. हो जाती है तो धनराशि क्या होगी यदि ब्याज दर में 5% की वृद्धि हो जाये?

  1. Rs.484

  2. Rs.504

  3. Rs.512

  4. Rs.560
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rs. 400 grows to Rs. 441 in 2 years, so the growth factor is 441/400 = 1.10. This means 10% total growth over 2 years, giving 5% simple interest annually. If rate increases by 5% to 10%, the amount after 2 years would be 400 × 1.20 = 480, or using compound: 400 × (1.10)² = 400 × 1.21 = 484. The answer suggests compound interest calculation.

Multiple choice

R borrowed Rs.1000 at 8% simple interest and S borrowed Rs.1400 at 5% simple interest after how much time the will have equal debts? R ने रू 1000 को 8% वार्षिक साधारण ब्याज की दर से तथा S ने रू 1400 को 5% वार्षिक साधारण ब्याज की दर से उधार लिया। कितने समय बाद दोनों का ऋण बराबर हो जाएगा?

  1. 15 years/वर्ष

  2. 25 years/वर्ष

  3. 40 years/वर्ष

  4. 50 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest formula: Amount = Principal + (P × R × T)/100. For R: Amount = 1000 + (1000 × 8 × t)/100 = 1000 + 80t. For S: Amount = 1400 + (1400 × 5 × t)/100 = 1400 + 70t. Setting equal: 1000 + 80t = 1400 + 70t, giving 10t = 400, so t = 40 years.

Multiple choice

The simple Interest on a certain sum for 8 months at 3% per annum is 1530 Rs. less than C.I. on the sum for 18 months at 2% perannum, compounded annualy. Find the sum. / किसी निश्चित राशि पर 3 प्रतिशत प्रतिवर्ष पर 8 माह का साधारण ब्याज उसी राशि पर 2 प्रतिशत प्रतिवर्ष चक्रवृद्धि ब्याज की दर पर 18 माह के ब्याज से 1530 रूपये कम है मूलधन ज्ञात कीजिए।

  1. 15000

  2. 150000

  3. 1800

  4. 180000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

SI = P×3/100×8/12 = 0.02P. CI = P(1+2/100)^1.5 - P ≈ 0.0303P. Difference ≈ 0.0103P = 1530. So P ≈ 153000/1.03 ≈ 148544. Closest option is 150000. The calculation is complex; 150000 is the best match among given choices.

Multiple choice

The compound interest on a sum for 2 years is Rs.832 and the simple interest on the same sum at the same rate for the same period is Rs.800.What is the rate of interest? एक धनराशि पर दो वर्षो का चक्रवृद्धि ब्याज 832 रू. है और इसी धनराशि पर इसी समान दर व समय में साधारण ब्याज 800 रू. है। ब्याज की दर क्या है ?

  1. 6%

  2. 8%

  3. 10%

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

The difference between CI and SI for 2 years is the interest on the first year's interest. Difference = 832 - 800 = 32. This equals P × r²/10000 where r is the rate. Also SI = P × r × 2/100 = 800. From these, we get r = 8%. Verification: P = 5000, SI = 800, CI = 832.

Multiple choice

Two equal sums were lent out at 9% and 7% simple interest, respectively, The sum of simple interest earned for the two loans at the end of 3 years is Rs.480. What is each sum equal to? दो समान धनराशि क्रमशः 9% और 7% साधारण ब्याज की दर से ऋण पर दी गयी। 3 वर्ष की अवधि के बाद उन पर अर्जित साधारण ब्याज का योग 480रू. होता है तो प्रत्येक धनराशि क्या है?

  1. Rs./रु.1000

  2. Rs./रु.1500

  3. Rs./रु.1800

  4. Rs./रु.2000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let each sum be x. Total simple interest = x(9% × 3) + x(7% × 3) = x(27% + 21%) = x(48%). Given total interest = Rs.480, so 0.48x = 480, giving x = 1000. Each sum is Rs.1000. This is correct.

Multiple choice

A sum of Rs. 22000 is divided into three parts such that the corresponding interest earned after 2 years, 3 years and 6 years may be equal. If the rates of simple interest are 6% p.a., 8% p.a. and 6% p.a. respectively, what is the sum of the smaller two parts that was lent? 22000 रू. की एक धनराशि को तीन भागों में इस तरह बांटा जाता है कि उनके द्वारा क्रमशः 2 वर्षों, 3 वर्षों और 6 वर्षों में प्राप्त ब्याज समान हों। यदि साधारण ब्याज की दरें क्रमशः 6% वार्षिक 8% वार्षिक और 6% वार्षिक हैं, उधार दी गयी दो छोटी राशियों का योग क्या है?

  1. Rs. 8000

  2. Rs. 12000

  3. Rs. 10000

  4. Rs. 15000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Set interests equal: x(2)(6) = y(3)(8) = z(6)(6). This gives 12x = 24y = 36z, so x = 2y and x = 3z. Total: x + y + z = 22000. Substituting y = x/2 and z = x/3 gives x + x/2 + x/3 = 22000, so 11x/6 = 22000, x = 12000. Then y = 6000, z = 4000. Sum of smaller two: 6000 + 4000 = 10000.

Multiple choice

What is the ratio of compound interest accrued in two years at 8% p.a. to the simple interest accrued in three years at 16% p.a., both calculated on the same sum of money? 2 वर्षों में 8% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज का 3 वर्षों में 16% वार्षिक ब्याज की दर से साधारण ब्याज में क्या अनुपात है, दोनों समान धनराशि के लिए गणित किये गये हैं?

  1. 12 : 25

  2. 26 : 75

  3. 18 : 25

  4. 31 : 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CI for 2 years at 8%: P(1.08)² - P = P(1.1664 - 1) = 0.1664P. SI for 3 years at 16%: P(3)(0.16) = 0.48P. Ratio = 0.1664P : 0.48P = 1664 : 4800 = 26 : 75. The key is calculating compound interest correctly and simplifying the ratio.