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

The respective ratio of the amount after 16.5 years and 17.5 years is 25:27; the interest being compounded annually. Find the rate of the interest charged per annum. 16.5 वर्ष तथा 17.5 वर्ष के पश्चात् प्राप्त मिश्रधनों का अनुपात क्रमशः 25: 27, जब ब्याज की गणना चकृवृद्धि वार्षिक हो। तो ब्याज की वार्षिक दर ज्ञात कीजिये।

  1. 10%

  2. 12%

  3. 8%

  4. 9%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using compound interest formula A = P(1 + r/100)^n, the ratio A17.5/A16.5 = (1 + r/100)^(17.5-16.5) = 1 + r/100 = 27/25. So r/100 = 2/25, giving r = 8%. Option C is correct.

Multiple choice

A person deposited a sum of Rs.x in a bank at 5% per annum simple interest. Another person deposited Rs.y at 8% per annum compound interest. After two years the difference of their interests will be Rs.232. Find the greater principal, if the ratio between x and y is 6 : 5.

  1. Rs.1000

  2. Rs.5000

  3. Rs.23200

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

SI on x: (x×5×2)/100=0.1x. CI on y for 2 years at 8%: y(1.08²-1)=y(1.1664-1)=0.1664y. Difference: 0.1664y-0.1x=232. Given x:y=6:5, let x=6k, y=5k: 0.1664(5k)-0.1(6k)=232 → 0.832k-0.6k=232 → 0.232k=232 → k=1000. y=5000, x=6000. Greater principal=6000.

Multiple choice

The rate of interest per annum at which the total simple interest of a certain capital for 1 year is equal to the total simple interest of the same capital at the rate of 5% per annum for 2 years, is वह ब्याज की दर जिस पर किसी निश्चित पूँजी पर 1 वर्ष में साधारण ब्याज उसी समान पूँजी पर 5% ब्याज की दर से 2 वर्षों में कुल साधारण ब्याज के बराबर है, है ?

  1. 2.5%

  2. 10%

  3. 25%

  4. 12.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the required rate be r% and capital be P. Simple interest for 1 year at r% = P × r/100. Simple interest for 2 years at 5% = P × 5 × 2/100 = P × 10/100. Equating: P × r/100 = P × 10/100 → r = 10%. Option B is correct.

Multiple choice

A person takes a loan of Rs.40000 partly from a bank at 10% p.a. and remaining from another bank at 12% p.a. He pays total interest of 4440 per annum. Amount of loan taken from the first bank (in Rs.) is- एक व्यक्ति रू. 40000 के ऋण का एक भाग वह 10% वार्षिक की दर पर एक बैंक से लेता है और 12% वार्षिक दर पर दूसरे बैंक से लेता है। वह कुल वार्षिक ब्याज के रूप में रू. 4440 का भुगतान करता है। तद्नुसार उसका पहले बैंक से लिया गया ऋण (रू. में) था-

  1. Rs./रु.22000

  2. Rs./रु.20000

  3. Rs./रु.18000

  4. Rs./रु.16000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the loan at 10%, so (40000-x) is at 12%. Total interest: 0.1x + 0.12(40000-x) = 4440. Simplifying: 0.1x + 4800 - 0.12x = 4440, giving -0.02x = -360, so x = 18000. Options A and B would give insufficient total interest, while D gives excess.

Multiple choice

If the compound interest on a certain sum for two years at 12% per annum is Rs 1908, the simple interest on it at the same rate for 2 years will be - यदि एक धनराशि पर दो वर्षो का 12% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज 1908 रू.हो, तो उसी दर पर दो वर्षो का साधारण ब्याज होगा-

  1. Rs./रु.1600

  2. Rs./रु.1650

  3. Rs./रु.1700

  4. Rs./रु.1800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let principal be P. CI for 2 years at 12%: P(1.12)² - P = 1908, so P(1.2544 - 1) = 1908, giving P = 1908/0.2544 = 7500. SI for 2 years at 12%: 7500 × 0.12 × 2 = 1800. Option A (1600) is 10% of P for 2 years, ignoring the actual rate.

Multiple choice

Sameer obtained a loan of Rs. 5000 against some security. If the rate of interest is 2.5% per annum compounded annually, find the amount paid by him at the end of three years? समीर कुछ प्रतिभूतियों पर 5000 रू. का ऋण प्राप्त करता है। यदि वार्षिक ब्याज की दर 2.5% प्रति वर्ष चक्रवृद्धि रूप संयोजित होने वाली हो, तो उसके द्वारा तीन वर्ष की समाप्ति पर चुकता की गई धनराशि ज्ञात कीजिए।

  1. Rs. 5384.45

  2. Rs. 5320.40

  3. Rs. 5402.50

  4. Rs. 5420.40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound interest formula: A = P(1 + r)^n. A = 5000 × (1.025)³ = 5000 × 1.07689 = Rs. 5384.45.

Multiple choice

Deepinder lent Rs 8200 to Jairaj for 16 years and Rs 4900 to Karna for 15 years on simple interest at the same rate of interest and received Rs 19446.5 in all from both of them as interest. What is the rate of interest per annum? दीपिंदर ने जयराज को 16 वर्षों के लिए 8200 रू. उधार दिए और करन को उसी दर पर 15 वर्षों के लिए 4900 रू. उधार दिए और दोनों से ब्याज के रूप में कुल 19446.5 रू. प्राप्त किए। वार्षिक ब्याज दर कितनी होगी?

  1. 10 %

  2. 10.5 %

  3. 9.5 %

  4. 11 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rate = r%. SI from Jairaj = 8200 × r × 16/100 = 1312r. SI from Karna = 4900 × r × 15/100 = 735r. Total SI = 1312r + 735r = 2047r = 19446.5. So r = 19446.5/2047 = 9.5%.

Multiple choice

A sum of money at compound interest will amount to Rs. 650 at the end of the first year and Rs. 676 at the end of the second year. The amount of money is- एक धनराशि चक्रवृद्धि ब्याज की दर पर प्रथम वर्ष के अंत में 650 रूपये और दूसरे वर्ष के अंत में 676 रूपये हो जाती है तो धनराशि है-

  1. Rs. 1300

  2. Rs. 650

  3. Rs. 1250

  4. Rs. 625
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If amount grows from Rs. 650 to Rs. 676 in one year, interest = Rs. 26. Rate = 26 ÷ 650 × 100 = 4%. Let principal be P, then P × 1.04 = 650, so P = 650 ÷ 1.04 = Rs. 625. Option A is incorrectly calculated as 650 × 2, option B is the first year's amount, and option C is a rough approximation.

Multiple choice

A man borrowed Rs. 9100 at 20% compound interest (compounded annually). He agreed to pay the money in 3 equal annual instalment, the first instalment to be made at the end of 1 year from the date of borrowing. What is the value of each instalment? एक व्यक्ति 9100 रू. की राशि 20% चक्रवृद्धि ब्याज की दर से (चक्रवृद्धि रूप से संयोजित) उधार लेता है। वह धनराशि को 3 बराबर वार्षिक किश्तों में चुकाने के लिए सहमत होता है, उधार लेने की तारीख से 1 वर्ष के अन्त में पहली किश्त चुकाई जाती है। प्रत्येक किश्त की राशि क्या है?

  1. Rs. 4320

  2. Rs. 4420

  3. Rs. 4440

  4. Rs. 4220
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal annual installments with compound interest, the present value of all installments equals the loan amount. Let each installment be x. The PV is x/(1.2) + x/(1.2)² + x/(1.2)³ = x(0.8333 + 0.6944 + 0.5787) ≈ 2.1064x. Setting 2.1064x = 9100 gives x ≈ 4320. Verification: 4320/1.2 = 3600, 4320/1.44 = 3000, 4320/1.728 = 2500; sum = 9100.

Multiple choice

Some amount out of Rs. 5000 was lent at 5% per annum and the remaining was lent at 4% per annum. If the total simple interest from both in 5 years was Rs. 1050. Calculate the sum lent at 4% per annum. 5000 रू. में से कुछ राशि 5% वार्षिक पर उधार दी गई और शेष को 4% वार्षिक ब्याज की दर से उधार दिया गया। यदि 5 वर्षों में दोनों से प्राप्त कुल साधारण ब्याज 1050 रू. है। 4% वार्षिक ब्याज दर दी गई धनराशि ज्ञात कीजिए।

  1. Rs. 5000

  2. Rs. 1000

  3. Rs. 925

  4. Rs. 4000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount lent at 4%. Then (5000-x) is lent at 5%. Simple interest: x×4×5/100 + (5000-x)×5×5/100 = 1050. This gives 0.2x + 1250 - 0.25x = 1050, so -0.05x = -200 and x = 4000. The remaining 1000 is lent at 5%.

Multiple choice

A certain sum at a certain rate of simple interest become to Rs. 1125 in 4 years and Rs. 1200 in 7 years. Find the rate of interest? एक निश्चित धनराशि साधारण ब्याज की एक निश्चित दर पर 4 वर्षो में 1125 रू. हो जाती है और 1200 रू. 7 वर्षो में हो जाती है। ब्याज की दर ज्ञात कीजिए।

  1. 2.43%

  2. 3.62%

  3. 4%

  4. 5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The simple interest for 3 years (from year 4 to year 7) is Rs. 1200-1125=Rs. 75. Annual interest is Rs. 25. In the first 4 years, total interest is 1125-P (where P is principal). So 4×25=1125-P, giving P=1025. Rate = (25/1025)×100 = 2.439%, which rounds to 2.43%.

Multiple choice

A recurring deposit of Rs. 10 is paid regularly each month for 24 months, and amounts to Rs. 257.50. what is the rate of interest? रू. 10 की आवर्ती जमा राशि 24 माह के लिए प्रत्येक माह में नियमित रूप से भुगतान की जाती है और 257.50 के बराबर है। ब्याज की दर क्या है?

  1. 6

  2. 7

  3. 9

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

For a recurring deposit, maturity value M = P×n + P×n(n+1)/2×r/12×1/100 where P is monthly installment, n is number of months, r is annual rate. Here: P = 10, n = 24, M = 257.50. Principal deposited = 10×24 = 240. Interest = 257.50 - 240 = 17.50. Using the formula: I = P×n(n+1)/2×r/12×1/100, we get 17.50 = 10×24×25/2×r/12×1/100. Solving: 17.50 = 25r, so r = 0.70 or 7%.

Multiple choice

What is the diference between simple interest and compount interest on a sum of Rs. 250000 for 2 years, when the rate of interest is 4%? 250000 रू. की एक धनराशि पर 2 वर्षों में, 4 प्रतिशत की ब्याजदर पर साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर है।

  1. Rs. 300

  2. Rs. 400

  3. Rs. 500

  4. Rs. 2500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest for 2 years at 4% on Rs. 2,50,000 is 250000×4×2/100 = Rs. 20,000. Compound interest: After 1 year, amount = 250000(1 + 4/100) = 250000×1.04 = Rs. 2,60,000. After 2 years, amount = 260000×1.04 = Rs. 2,70,400. CI = 270400 - 250000 = Rs. 20,400. Difference = CI - SI = 20400 - 20000 = Rs. 400.