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

Find the compound interest on Rs. 23520 at the rate of 4% for 2 years compounded annually. 23520 रुपये पर 2 साल के लिए चक्रवृद्धि दर 4% की दर से चक्रवृद्धि ब्याज ज्ञात कीजिये ।

  1. Rs. 1991.232

  2. Rs. 1199.232

  3. Rs. 1919.232

  4. Rs. 1900.232
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = ₹23,520, rate = 4%, time = 2 years. After year 1: Amount = 23520 × 1.04 = ₹24,460.80. After year 2: Amount = 24460.80 × 1.04 = ₹25,439.232. Compound Interest = 25439.232 - 23520 = ₹1,919.232. Option C is correct. Alternatively: CI = P[(1 + r)^n - 1] = 23520[(1.04)² - 1] = 23520[1.0816 - 1] = 23520 × 0.0816 = ₹1,919.232.

Multiple choice

A tradesman marks his goods with two types of prices one for cash sale and the other for six month credit. What ratio should the prices bear to each other, allowing simple interest at 5% per annum? एक व्यापारी अपनी वस्तुओं पर दो प्रकार के अंकित मूल्य रखता है। एक नकद खरीददारों के लिए है तथा दूसरे छः महीने की उधार वालों के लिए है। यदि साधारण ब्याज की दर 5% वार्षिक हो, तो दोनों प्रकार के अंकित मूल्यों में अनुपात ज्ञात कीजिए।

  1. 40 : 41

  2. 20 : 21

  3. 19 : 18

  4. 7 : 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 6 months credit at 5% per annum simple interest, the interest charged = 5% × 6/12 = 2.5%. If cash price is P, then credit price must include this interest: P + 2.5% of P = 1.025P. The ratio of cash price to credit price = P : 1.025P = 1 : 1.025 = 40 : 41 after multiplying by 40.

Multiple choice

Any amount becomes 500 in 4 years at the rate of compound interest and becomes 800 in 8 years then what is the principal? कोई राशि चक्रवृद्धि ब्याज की दर से चार वर्षों में 500 रू. तथा 8 वर्षों में 800 रू. हो जाए तो वह राशि क्या है?

  1. 212.50

  2. 312.50

  3. 325.50

  4. 333
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Amount becomes 500 in 4 years and 800 in 8 years. Let P = principal. P(1+r)⁴ = 500, P(1+r)⁸ = 800. Dividing: (1+r)⁴ = 800/500 = 8/5. So P(8/5) = 500, P = 500 × 5/8 = 312.50. Verification: 312.50(8/5) = 500, and 500(8/5) = 800. Other options don't work.

Multiple choice

An amount at compound interest doubles itself in 4 years .In how many years will the amount become 8 times itself? कोई मूलधन चक्रवृद्धि व्याज की दर पर 4 वर्षों में स्वयं का दुगुना हो जाता है |कितने वर्षों में यही मूलधन स्वयं का 8 गुना हो जाएगा ?

  1. 8 years/वर्ष

  2. 12 years/वर्ष

  3. 16 years/वर्ष

  4. 24 years/वर्ष
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If amount doubles in 4 years, it becomes 2 times. To become 8 times (which is 2^3), we need 3 such 4-year periods, so total time is 3 × 4 = 12 years. In compound interest, if money doubles in t years, it becomes 2^n times in n × t years.

Multiple choice

600 amount to Rs. 740 in 5 years at a certain rate of simple interest. If the rate of interest is increased by 3 % . what will be the amount then ? 600 रुपए की राशि 5 वर्षो में 740 हो जाती है यदि ब्याज की दर को 3% बढ़ाया जाता है तो अब राशि ज्ञात कीजिये?

  1. 800

  2. 856

  3. 930

  4. 830
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First, find the original rate: Interest = 740-600 = 140, so rate = (140×100)/(600×5) = 14000/3000 = 4.67%. New rate = 4.67% + 3% = 7.67%. New interest = (600×7.67×5)/100 = 600×0.3835 = 230.1. New amount = 600 + 230.1 ≈ 830. The key is to calculate the original rate first, then add 3% to find the new amount.

Multiple choice

Rs.500 was invested at 12 % per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the sum of the interests on both the sums after 4 years is Rs.480, find the later sum of money? 500 रु की राशि 12% के वार्षिक साधारण ब्याज पर निवेश की जाती है और कुछ और राशि भी 10% की वार्षिक साधारण ब्याज पर निवेश की जाती है. दोनों राशि के ब्याज का योग 4 वर्ष बाद 480 रु है. तो बाद वाली राशि क्या थी?

  1. Rs.450

  2. Rs.750

  3. Rs.600

  4. Rs.550
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest from first sum: P = 500, R = 12%, T = 4 years. SI = (500 × 12 × 4)/100 = Rs. 240. Total interest = Rs. 480, so interest from second sum = 480 - 240 = Rs. 240. For second sum: SI = 240, R = 10%, T = 4. So P = (240 × 100)/(10 × 4) = Rs. 600.

Multiple choice

A certain amount earns simple interest of Rs 1250 after 6 years .Had the interest been 2 % more how much more interest would it have earned?

  1. Rs.45

  2. Rs.56

  3. Rs.42

  4. can't be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To calculate the additional interest earned at 2% more rate, we need the principal amount. The formula for additional interest is: Additional Interest = (Principal × Rate Difference × Time) / 100 = (P × 2 × 6) / 100 = 0.12P. Without knowing the principal amount (P), we cannot determine the exact additional interest. Options A, B, and C give specific values but cannot be calculated without the principal.

Multiple choice

A sum of Rs. 2550 is borrowed to be paid back in two years by two equal instalments.If rate of interest 4% per annm compound interest is allowed,each instalments will be of - एक 2550 रू. की धनराशि दो वर्षो में दो समान किस्त में देय उधार ली जाती है |यदि ब्याज दर 4% प्रतिवर्ष चक्रवृद्धि ब्याज देय है तो प्रत्येक किस्त होगी-

  1. 1775

  2. 1350

  3. 1352

  4. 1400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let each installment = x. Present value of first installment (paid after 1 year) = x/(1.04). Present value of second installment (paid after 2 years) = x/(1.04)^2. Sum = 2550. Solving: x(1/1.04 + 1/1.0816) = 2550. x(0.9615 + 0.9246) = 2550. x(1.8861) = 2550. x ≈ 1352. This matches option C.

Multiple choice

The difference between compound interest and simple interest on Rs. 20000 for 3 years at 10% p.a. is-

  1. Rs. 880

  2. Rs. 420

  3. Rs. 620

  4. Rs. 660
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest = P×R×T/100 = 20000×10×3/100 = Rs. 6000. Compound Interest = P[(1+R/100)^T - 1] = 20000[(1.1)^3 - 1] = 20000[1.331 - 1] = Rs. 6620. Difference = 6620 - 6000 = Rs. 620. The key is that compound interest earns interest on interest, creating a larger amount over time.

Multiple choice

What will be the amount if a sum of Rs. 5000 is placed at compound interest for 3 years while rate of interest for the first second and third year is 2,3 and 4 percent respectivly? 5000 रू. को यदि तीन वर्षों के लिये क्रमशः 2% 3% और 4% प्रतिवर्ष की दर से चक्रवृद्धि ब्याज के लिये लगाया गया तो मिश्रधन होगा?

  1. Rs./रू.5643.12

  2. Rs./रू.5463.12

  3. Rs./रू.6413.12

  4. Rs./रू.5594.12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Compound interest with varying rates: calculate year by year. After year 1 (2%): 5000 × 1.02 = 5100. After year 2 (3%): 5100 × 1.03 = 5253. After year 3 (4%): 5253 × 1.04 = 5463.12. The amount is Rs. 5463.12.

Multiple choice

Kamal lent out Rs. 60000. Out of these some part at 5% and remaining at 4% at simple interest. If total annual interest is Rs. 2560. What is the amount at 4% ?

  1. Rs. 40000

  2. Rs. 44000

  3. Rs. 30000

  4. Rs. 45000

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

Let the amount at 4% be Rs. x. Then the amount at 5% is Rs. (60000 - x). Total interest: 0.04x + 0.05(60000 - x) = 2560. Solving: 0.04x + 3000 - 0.05x = 2560, so -0.01x = -440, giving x = 44000. Therefore, Rs. 44,000 was lent at 4%. Option A (Rs. 40,000) would give interest of Rs. 2,600, and Option C (Rs. 30,000) would give interest of Rs. 2,700 - neither matches the required Rs. 2,560.

Multiple choice

Arun borrowed a certain sum from Sandeep at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4800 as compound interest but paid Rs. 4000 only as simple interest. Find the rate of interest.

  1. 20%

  2. 10%

  3. 40%

  4. Cannot be determined

  5. 50%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years at rate r%, CI - SI = P × r²/100². Given CI - SI = 4800 - 4000 = 800. Also, SI = P × r × 2/100 = 4000, so P × r = 200000. Then 800 = 200000 × r/100, giving r = 40%. The key insight is the difference between compound and simple interest for 2 years is P(r/100)².

Multiple choice

Rs. 15000 were invested for 5 years in Scheme A which offeres simple interest the rate of 14% p.a. The amount received after 5 years and some additional money , is then invested in Scheme B , for 2 years , which offers compound interest ( compounded annually ) at the rate of 20% p.a. If the compound interest received from Scheme B after 2 years is Rs. 14080 . What was the additional amount invested in Scheme B apart from the amount from Scheme A ?

  1. 4500

  2. 5500

  3. 5000

  4. 6500

  5. 7000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Scheme A से प्राप्त राशि = 15000 + (15000 × 14% × 5) = 15000 + 10500 = 25500। Scheme B में मूलधन P और चक्रवृद्धि ब्याज 2 वर्षों के लिए 20% वार्षिक दर से = 14080। चक्रवृद्धि ब्याज सूत्र से: P × (1.20)^2 - P = 14080 → P × 1.44 - P = 14080 → 0.44P = 14080 → P = 32000। अतिरिक्त राशि = 32000 - 25500 = 6500। यह एक दो-चरण ब्याज गणना समस्या है जिसमें पहले साधारण ब्याज फिर चक्रवृद्धि ब्याज की गणना करनी होती है।

Multiple choice

The rate of interest on a certain sum is 5% for first 2 years, 6% for next 3 years and 8% for further years. After 9 years, 3000 Rs. is obtained as total interest on that sum. Find the sum./किसी धनराशि पर पहले 2 वर्षों के लिए ब्याज की दर 5% वार्षिक, अगले 3 वर्षों के लिए 6% वार्षिक तथा अगले वर्षों के लिए 8% वार्षिक है। उस धन पर 9 वर्ष बाद कुल ब्याज 3000 रू. प्राप्त होता है। धनराशि ज्ञात कीजिए।

  1. Rs. 10000

  2. Rs. 8000

  3. Rs. 7000

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

Let principal be P. Total simple interest = P×(5/100)×2 + P×(6/100)×3 + P×(8/100)×4 = P×(0.1 + 0.18 + 0.32) = 0.6P. Given total interest = Rs. 3000, so 0.6P = 3000, P = Rs. 5000. Option A (Rs. 10000) would give Rs. 6000 interest at these rates. Option C (Rs. 7000) would give Rs. 4200 interest.

Multiple choice

What is the annual instalment to discharge a debt of Rs. 2210 due in 4 years at 7% simple interest? एक 2210 रू. के ऋण को 4 वर्षों में 7% की सा. ब्याज की दर से वार्षिक किस्त क्या होगी?

  1. 450

  2. 500

  3. 600

  4. 750
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal annual instalments at simple interest: let instalment be x. Amount paid = x + x(1 + r/100) + x(1 + 2r/100) + x(1 + 3r/100). At 7%: x(1 + 1.07 + 1.14 + 1.21) = 2210. This gives x(4.42) = 2210, so x = 500. Each instalment of Rs. 500 will discharge the debt in 4 years.