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 sum was invested at a certain rate of interest for 8 years. If the sum were invested at 5% more rate of interest, it would have Rs. 220 more. What is the sum (in Rs)?

  1. 330

  2. 350

  3. 4400

  4. 550

  5. 650
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be the principal sum at rate R% for 8 years. Simple Interest = P × R × T / 100. If rate increases by 5%, the extra interest earned is P × 5 × 8 / 100 = 2P/5. Given this equals Rs. 220, so P = 550. Therefore, Rs. 550 was invested.

Multiple choice

Mrs. Reema invested Rs. 10000 at 5% per annum compounded annually. What is the amount of interest received by her after 2 years?

  1. Rs. 1500

  2. Rs. 1100

  3. Rs. 1050

  4. Rs. 1125

  5. Rs. 1025
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Compound interest for 2 years at 5% annually on Rs. 10000: Year 1 interest = 10000 x 5% = Rs. 500. New principal = 10000 + 500 = Rs. 10500. Year 2 interest = 10500 x 5% = Rs. 525. Total interest = 500 + 525 = Rs. 1025. Alternatively using formula: CI = P[(1 + r)^n - 1] = 10000[(1.05)^2 - 1] = 10000[1.1025 - 1] = 10000 x 0.1025 = Rs. 1025.

Multiple choice

A sum of money was invested for 14 years was in a Scheme A which offers simple interest at a rate of 8% p.a. The amount received from Scheme A after 14 years was then invested for two years in Scheme B which offers compound interest ( compounded annually ) at a rate of 10 % p.a. If the interest received from Scheme B was Rs. 6678, what was the sum invested in Scheme B?

  1. Rs. 31,500

  2. Rs. 31,800

  3. Rs. 30,500

  4. Rs. 30,800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let principal be P. After Scheme A (14 years, 8% SI): Amount = P(1 + 0.08×14) = 2.12P. In Scheme B (2 years, 10% CI): Interest = 2.12P[(1.10)² - 1] = 2.12P × 0.21 = Rs. 6678. So 2.12P = 6678/0.21 = Rs. 31,800. The key is tracking how the amount from one scheme becomes the principal for the next.

Multiple choice

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum? 15000 की धनराशि पर 2 वर्षों के लिए साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर रू. 150 है। ब्याज की वार्षिक दर क्या है?

  1. 8%

  2. 12%

  3. 10%

  4. 15%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years, the difference between compound interest and simple interest is P*r²/10000. Setting 15000*r²/10000 = 150 gives r² = 100, so r = 10%. The key insight is that CI-SI for 2 years depends only on principal and rate squared.

Multiple choice

Rs.800 becomes Rs.956 in 3 years with certain rate of simple interest if rate of interest is increased by 4% then find the new amount after the same time period on same sum. रू.800 तीन वर्षों में किसी निश्चित साधारण ब्याज की दर से रू.956 हो जाती है यदि ब्याज दर को 4 प्रतिशत बढ़ा दिया जाए तो समान धनराशि पर उतने ही समय के बाद प्राप्त धनराशि ज्ञात कीजिये ।

  1. Rs./रू.952

  2. Rs./रू.1052

  3. Rs./रू.1152

  4. Rs./रू.1952
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interest for 3 years = 956 - 800 = Rs. 156. Annual interest = 156/3 = Rs. 52. Rate = (52/800) × 100 = 6.5%. New rate = 10.5%, new annual interest = 800 × 0.105 = Rs. 84. New amount = 800 + (84 × 3) = Rs. 1052. Option B is correct.

Multiple choice

Find the sum on which simple interest is Rs.1 for one day with 5% rate per annum. वह धनराशि ज्ञात कीजिये जिस पर 5 प्रतिशत वर्षिक साधारण ब्याज दर से 1 रू प्रतिदिन का ब्याज प्राप्त होता है ।

  1. Rs./रु.3650

  2. Rs./रु.36500

  3. Rs./रु.730

  4. Rs./रु.7300
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Daily interest at 5% per annum = P × (5/100) × (1/365) = 1. Solving: P = 100 × 365/5 = Rs. 7300. Option D is correct.

Multiple choice

The difference between simple interest and compound interest on a sum of money at 5% p.a. for 2 years is Rs. 100 the sum of money must be दो वर्षों के लिए साधारण ब्याज और चक्रवृद्धि ब्याज का अन्तर 5% ब्याज दर से रू. 100 है। तो आरम्भिक धनराशि ज्ञात कीजिए।

  1. Rs./रू. 35000

  2. Rs./रू. 41000

  3. Rs./रू. 40000

  4. Rs./रू. 45000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years at 5%, CI - SI = P × (R/100)². Here: 100 = P × (5/100)² = P × 0.0025, so P = 100/0.0025 = Rs. 40,000. This direct formula applies when the difference between CI and SI is asked for exactly 2 years.

Multiple choice

A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself? एक धनराशि, चक्रवृद्धि ब्याज पर 3 वर्षों में तीन गुनी हो जाती है। तदनुसार, वह अपनी मूल राशि की 9 गुनी कितने वर्षों में हो जाएगी?

  1. 9

  2. 27

  3. 6

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In compound interest, if an amount becomes n times in t years, it becomes n^k times in k×t years (geometric progression). Here, amount becomes 3 times in 3 years. To become 9 times (which is 3²), it takes 2×3 = 6 years. Option A (9) incorrectly uses linear progression, while option B (27) would give 27 times (3³), not 9 times.

Multiple choice

The simple interest on Rs 4000 in 3 years at the rate of a% per annum equals the simple interest on Rs 5000 at the rate of 12 % per annum in 2 years. The value of a is- a प्रतिशत प्रति वर्ष की दर से 4000 रूपये का 3 वर्ष का साधारण ब्याज, 12 प्रतिशत प्रति वर्ष की दर से 5000 रूपये पर 2 वर्ष के साधारण ब्याज के बराबर है। तो a का मान है-

  1. 8%

  2. 10%

  3. 9%

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

SI on Rs 4000 at a% for 3 years = (4000 × a × 3)/100 = 120a. SI on Rs 5000 at 12% for 2 years = (5000 × 12 × 2)/100 = 1200. Given 120a = 1200, so a = 10%. Option B is correct.

Multiple choice

A sum of money is borrowed and paid back in two annual equal instalments of Rs 8820, allowing 5% per annum compound interest. Find the sum borrowed? एक व्यक्ति ने कुछ राशि उधार ली और उसे 8820रू. प्रतिवर्ष की दो समान किस्तों में लौटाया। यदि चक्रवृद्धि ब्याज 5 प्रतिशत वार्षिक दर से लिया जाता हो, तो उधार ली गई कुल राशि ज्ञात कीजिए?

  1. 17640

  2. 16980

  3. 16400

  4. 16200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the sum borrowed. After 1st year: P × 1.05 - 8820 = remaining principal. After 2nd year: (P × 1.05 - 8820) × 1.05 = 8820 (final payment). Solving: P × 1.1025 - 8820 × 1.05 = 8820, so P × 1.1025 = 8820 + 9261 = 18081, giving P = 18081 / 1.1025 = 16400. Each installment includes both principal and compound interest.

Multiple choice

A person lent Rs. 8000 partly at the rate of 5% and partly at the rate of 6% per annum simple interest. The total interest after 2 years is Rs. 820 then in which ratio will Rs. 8000 is to be divided? एक व्यक्ति 8000 रूपए का कुछ भाग 5% वार्षिक और शेष भाग 6% वार्षिक साधारण ब्याज की दर पर उधार देता है। दो वर्ष बाद कुल ब्याज 820 रूपए प्राप्त होता है तो 8000 रूपए को किस अनुपात में बांटना होगा?

  1. 13 : 5

  2. 12 : 5

  3. 15 : 4

  4. 7 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Rs. x be invested at 5% and Rs. (8000-x) at 6%. Total simple interest after 2 years = 820. So: x × 0.05 × 2 + (8000-x) × 0.06 × 2 = 820. This simplifies to 0.1x + 960 - 0.12x = 820, giving -0.02x = -140, so x = 7000. The amounts are 7000 and 1000, giving ratio 7:1. Options A, B, and C are incorrect ratios.

Multiple choice

What will be the annual installment to discharge a debt of Rs. 58000 at the rate of 8% simple interest in a period of 5 years? 58000 रू. का कर्ज 8% साधारण व्याज की दर से 5 वर्ष में चुकाने के लिए वार्षिक किश्त क्या होगी?

  1. 10000

  2. 9500

  3. 10500

  4. 11200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal annual installments with simple interest: Each installment of Rs. X is paid at year-end. The first installment (at end of year 1) earns interest for 4 more years, so its contribution = X + X×8%×4 = 1.32X. Similarly: 2nd: 1.24X, 3rd: 1.16X, 4th: 1.08X, 5th: X. Total = 5X + 8%×X×(4+3+2+1+0) = 5X + 0.08X×10 = 5.8X = Rs. 58000. So X = 58000/5.8 = Rs. 10000. Option A is correct. Options B (9500), C (10500), and D (11200) don't satisfy the equation.