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

A loan of Rs. 68740 is paid back in three annual installments second installment is twice of first and third is three-fourth of second installment. If for the remaining time, the rate of compound interest be 10% per annum on each installment. Find the second installment. 68740 रू. का कर्ज तीन वार्षिक किश्तों में चुकाया जाता है। दूसरी किश्त पहली किश्त का दोगुना है और तीसरी किश्त दूसरी किश्त का तीन चौथाई है। यदि शेष समय के लिए प्रत्येक किश्त पर 10% वार्षिक चक्रवृद्धि ब्याज की दर उपचयित है। दूसरी किश्त ज्ञात कीजिए।

  1. Rs. 32768

  2. Rs. 37682

  3. Rs. 37862

  4. Rs. 37268
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let installments be x, 2x, (3/4)(2x) = 1.5x. Using present value at 10% compound interest: x/1.1 + 2x/1.1² + 1.5x/1.1³ = 68740. Solving gives x ≈ 18634. Second installment = 2x ≈ 37268. Option D is correct.

Multiple choice

The difference of simple interest on Rs. 7500 from two different sources for three years is Rs. 13.50. Find the difference of the interest rates. 7500 रू. पर तीन वर्षों में दो विभिन्न श्रोतों से प्राप्त साधारण ब्याज में अन्तर 13.50 रू. है। ब्याज दरों में अन्तर ज्ञात कीजिए।

  1. 0.02%

  2. 0.03%

  3. 0.04%

  4. 0.06%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest = P × R × T / 100. Difference in interests = P × T × (R1 - R2) / 100 = 7500 × 3 × ΔR / 100 = 225 × ΔR = 13.50. Therefore ΔR = 13.50 / 225 = 0.06%. Option D is correct.

Multiple choice

The sum lent at 5% per annum (i.e. 365 days) simple interest, that produces interest, of Rs. 40.0 per day is किसी धनराशि को 5% वार्षिक (365 दिन) साधारण ब्याज की दर से उधार दिया जाता है, जिससे उसे ब्याज के रूप में 40.0 रू. प्रतिदिन प्राप्त होते हैं। धनराशि बताइए।

  1. 292000

  2. 29200

  3. 229000

  4. 252000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Daily interest = Rs. 40. Annual interest at 5% = 40 × 365 = Rs. 14,600. If principal is P, then 5% of P = 14,600. Therefore P = 14,600 × 100/5 = Rs. 2,92,000.

Multiple choice

A man borrows Rs. 21000 at 10% compound interest. How much he has to pay equally at the end of each year, to settle his loan in two years?

  1. Rs. 12000

  2. Rs. 12100

  3. Rs. 12200

  4. Rs. 12300
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let annual payment = x. After 1st year: 21000×1.1 - x = 23100 - x. After 2nd year: (23100-x)×1.1 - x = 25410 - 2.1x = 0. Solving: 25410 = 2.1x, x = 12100. Verification: Year 1: 23100-12100=11000; Year 2: 11000×1.1-12100=12100-12100=0.

Multiple choice

Rajesh took Rs. 38400 from Seema at 10% rate of Simple interest and give it to Suresh who gives 12.5% rate of compound interest compound annually. If Rajesh gives the money to Suresh for 3 years and return to Seema immediately. Find the profit of Rajesh.

  1. 4252

  2. 4500

  3. 3852.5

  4. 4755

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

Rajesh borrows Rs. 38400 at 10% simple interest for 3 years. Using SI = PRT/100, interest = 38400 * 10 * 3 / 100 = Rs. 11520. Total repayment to Seema = 38400 + 11520 = Rs. 49920. He lends the same amount at 12.5% compound interest annually for 3 years. Using A = P(1+r/100)^n, amount = 38400 * (1.125)^3 = 38400 * 1.4238 = Rs. 54975. Profit = 54975 - 49920 = Rs. 4755.

Multiple choice

The compound interest and simple interest for two years on a certain sum of money at a certain rate of interest is 157.5. Find the principal if rate of interest is 15%. एक निश्चित धनराशि पर निश्चित ब्याज की दर से दो वर्षों के चक्रवृद्धि ब्याज और साधारण ब्याज में अंतर 157.5 है। मूलधन ज्ञात कीजिए यदि ब्याज की दर 15 प्रतिशत है।

  1. Rs. 6000

  2. Rs. 7000

  3. Rs. 8000

  4. Rs. 15750
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, CI - SI = P × (r/100)^2. Given CI - SI = 157.5 and r = 15%. So 157.5 = P × (15/100)^2 = P × 0.0225. Therefore P = 157.5/0.0225 = 157.5 × 10000/225 = 1575000/225 = 7000. Verification: SI for 2 years = 7000 × 0.15 × 2 = 2100. CI for 2 years = 7000 × (1.15)^2 - 7000 = 9257.50 - 7000 = 2257.50. CI - SI = 2257.50 - 2100 = 157.50. ✓

Multiple choice

The amount on a certain sum at a certain rate of compound interest for the second year and third year is Rs. 21780 and Rs. 23958 respectively. Find the compound interest at the same rate of interest in two years. /एक निश्चित धनराशि पर निश्चित ब्याज की दर से क्रमशः द्वितीय वर्ष और तृतीय वर्ष का मिश्रधन क्रमशः 21780 रू. और 23958 रू. हो जाता है। दो वर्ष में उसी ब्याज दर पर उपचित चक्रवृद्धि ब्याज ज्ञात कीजिए।

  1. Rs. 3280

  2. Rs. 3580

  3. Rs. 3680

  4. Rs. 3780
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Amount after 2nd year = 21780, after 3rd year = 23958. Interest for 3rd year = 23958 - 21780 = 2178. This is the interest on 21780 at rate r%. So r = (2178/21780) × 100 = 10%. Interest for 2nd year = 21780 - Amount after 1st year. Let A1 = amount after 1st year. Then A1 × 1.10 = 21780, so A1 = 19800. Principal = 19800/1.10 = 18000. CI for 2 years = 21780 - 18000 = 3780. ✓

Multiple choice

A sum of money becomes (7/6) of itself in 3 years at a certain rate of simple interest. The rate per annum is एक धनराशि 3 वर्षों में किसी निश्चित साधारण ब्याज की दर से स्वयं का (7/6) गुना हो जाती है | वार्षिक ब्याज की दर है

  1. 5(5/9)%

  2. 6(5/9)%

  3. 18%

  4. 25%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple Interest formula: SI = P × R × T / 100. Amount after 3 years = P + SI = P + (P × R × 3)/100 = P(1 + 3R/100). Given amount = (7/6)P, so (7/6)P = P(1 + 3R/100). Dividing by P: 7/6 = 1 + 3R/100, giving 3R/100 = 1/6, so R = 100/18 = 50/9 = 5(5/9)% per annum. Option B gives 6.67%, Option C gives 18%, and Option D gives 25% - all too high for the given growth.

Multiple choice

A sum becomes Rs.2916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be एक धनराशि 2 वर्षों में 8 % वार्षिक चक्रवृद्धि ब्याज की दर से रु.2916 हो जाती है | उसी धनराशि पर 9% वार्षिक ब्याज की दर से 3 वर्षों में साधारण ब्याज होगा

  1. Rs./रु.600

  2. Rs./रु.675

  3. Rs./रु.650

  4. Rs./रु.625
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For compound interest: A = P(1 + r/100)ⁿ. Given A = Rs. 2916, r = 8%, n = 2 years. So 2916 = P(1.08)² = P × 1.1664, giving P = 2916/1.1664 = Rs. 2500. For simple interest at 9% for 3 years on Rs. 2500: SI = 2500 × 9 × 3 / 100 = Rs. 675. Option A requires principal Rs. 2500 at 8%, Option C would need Rs. 2500 at 8.67%, and Option D is a calculation error.

Multiple choice

The difference between compound interest and simple interest on a certain sum at 12% p.a. for two years is Rs. 360. What will be the value of the amount at the end of 2 years when rate of interest is compounded annually. एक निश्चित धनराशि पर 2 वर्षों में 12% वार्षिक ब्याज की दर से दो वर्ष में चक्रवृद्धि ब्याज और साधारण ब्याज में अन्तर 360 रू. है। 2 वर्ष के अन्त में मिश्रधन क्या होगा यदि ब्याज की दर वार्षिक चक्रवृद्धि ब्याज के रूप से संयोजित होती है।

  1. 31360

  2. 33160

  3. 33610

  4. 36310
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Difference between CI and SI for 2 years at 12% = P(12/100)² = 360. This gives P × 0.0144 = 360, so P = 25000. Amount after 2 years = P(1 + 12/100)² = 25000 × 1.2544 = 31360. Options B, C, D are incorrect.

Multiple choice

Find the compound interest on Rs. 16000 in three years at 5% rate of interest annually. / 16000 रू. पर 3 वर्ष में 5% वार्षिक ब्याज की दर से चक्रवृद्धि ज्ञात कीजिए।

  1. 2252

  2. 2522

  3. 2255

  4. 2225
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Compound interest formula: A = P(1 + r/100)^n. Here P = 16000, r = 5%, n = 3. A = 16000(1.05)³ = 16000 × 1.157625 = 18522. CI = A - P = 18522 - 16000 = 2522.

Multiple choice

If amount of a sum becomes Rs 12575 in two years and Rs 13125 in four years with simple rate of interest. Find the sum.

  1. Rs.12000

  2. Rs.11025

  3. Rs.11500

  4. Cannot be determined

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

Let the principal be P and rate be R%. Amount after 2 years = P + (P × R × 2)/100 = 12575. Amount after 4 years = P + (P × R × 4)/100 = 13125. Subtracting: (P × R × 2)/100 = 13125 - 12575 = 550. This means interest for 2 years is Rs 550. From first equation: P + 550 = 12575, so P = 12025. But 12025 is not in options A, B, C, or D. Option E (None of these) is correct.

Multiple choice

An equal principal was invested in two banks first offering 15% simple interest and second offering compound interest of 20%. If the difference of interest from both banks after 3 years was Rs. 417. Find the principle invested in each bank.

  1. Rs. 1800

  2. Rs. 1500

  3. Rs. 2400

  4. Rs. 3000

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

SI at 15% for 3 years: Interest = P × 0.15 × 3 = 0.45P. CI at 20% for 3 years: Amount = P × 1.20³ = 1.728P, Interest = 0.728P. Difference = 0.728P - 0.45P = 0.278P = 417. Solving: P = 417/0.278 = 1500.

Multiple choice

If difference between simple interest on a certain-sum at 4% for 6 years and 5% for 4 years is Rs. 48. Find the sum. यदि एक धनराशि पर 6 वर्ष में 4% की दर से और 4 वर्ष में 5% की दर से साधारण ब्याज में अन्तर 48 रू. है। धनराशि ज्ञात कीजिए।

  1. Rs. 800

  2. Rs. 1200

  3. Rs. 1600

  4. Rs. 1000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let sum be P. Difference: P×4×6/100 - P×5×4/100 = 48. This gives P(0.24 - 0.20) = 48, so 0.04P = 48, and P = 48/0.04 = 1200.