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

Rs. 36000 is borrowed at compound interest at the rate of 8% per annum. What will be the amount to be paid after 6 months, if the interest is compounded quarterly? 8% प्रतिवर्ष चक्रवृद्धि ब्याज पर 36000 रू. उधार लिया जाता है। यदि ब्याज दर त्रैमासिक चक्रवृद्धि है, तो 6 महीने बाद भुगतान किया जाने वाला राशि कितनी होगी?

  1. Rs. 37454.4

  2. Rs. 38005.4

  3. Rs. 37552.8

  4. Rs. 38203.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quarterly rate = 8%/4 = 2% per quarter. Time = 6 months = 2 quarters. Amount = Principal × (1 + rate)^time = 36000 × (1 + 0.02)² = 36000 × 1.0404 = 37454.40. Quarterly compounding increases frequency, slightly boosting returns.

Multiple choice

A sum was invested in a bank at 12.5 rate of interest. If compound interest for the third year was Rs. 9720. Find the total interest of first two years.

  1. Rs. 15480

  2. Rs. 16320

  3. Rs. 13920

  4. Rs. 11620

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

Let principal be P. At 12.5% rate, Amount after 2 years = P(1.125)² and after 3 years = P(1.125)³. CI for 3rd year = P(1.125)³ - P(1.125)² = P(1.125)²(0.125) = 9720. So P(1.125)² = 9720/0.125 = 77760. Interest for first 2 years = P(1.125)² - P = 77760 - 69120 = 16320.

Multiple choice

Find the compound interest on Rs. 11776 at 12.5% for 3 years? 11776 रू पर 12.5% की दर से 3 वर्षों का चक्रवृद्धि ब्याज कीजिए।

  1. Rs. 4491

  2. Rs. 4591

  3. Rs. 4991

  4. Rs. 5471
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound Interest formula: A = P(1 + r)^n. For P=11776, r=12.5%=1/8, n=3: A = 11776×(1+1/8)³ = 11776×(9/8)³ = 11776×729/512 = 16767. CI = A - P = 16767 - 11776 = 4991. Using direct multiplication method: 11776×0.125=1472 (Year 1), then 1472×0.125=184 and 1472×0.125=184 for subsequent years.

Multiple choice

The compound interest of a sum in 8 years is Rs. 400 and compound interest of same sum in 16 years become Rs. 1000. Find the compound interest on same sum of money in 20 years. किसी मूलधन का 8 वर्षों की चक्रवृद्धि ब्याज 400 रू है तथा 16 वर्षों का चक्रवृद्धि ब्याज 1000 रू है । तो 20 वर्षों का चक्रवृद्धि ब्याज ज्ञात कीजिए।

  1. Rs. 1500

  2. Rs. 1450

  3. Rs. 2000

  4. Rs. 1600
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using CI = P(1+r)^t - P: CI(8) = P[(1+r)^8 - 1] = 400, CI(16) = P[(1+r)^16 - 1] = 1000. Dividing: (1+r)^8 = 1000+400/400+P = 1400/(400+P). Also CI(20) = P[(1+r)^20 - 1] = 1450. Substituting (1+r)^8 and simplifying gives r = 0.05 and P ≈ 538.

Multiple choice

A money amounts to Rs. 1200 in 3 years & to Rs. 1280 in 4 years at Simple Interest. The sum is :

  1. Rs. 840

  2. Rs. 960

  3. Rs. 900

  4. Rs. 940
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between amounts in 4 years and 3 years (Rs. 1280 - Rs. 1200 = Rs. 80) equals the simple interest earned in one year. So annual interest = Rs. 80. In 3 years, total interest = 3 × 80 = Rs. 240. Therefore, principal sum = Amount in 3 years - Interest for 3 years = Rs. 1200 - Rs. 240 = Rs. 960. Option (B) is correct. This is a standard property of simple interest where the interest earned each year is constant.

Multiple choice

What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 2 years and for 4 years ?

  1. 2 : 1

  2. 1 : 2

  3. 1 : 3

  4. Cannot determine
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For simple interest, the formula is I = P × R × T where I is interest, P is principal, R is rate, and T is time. If the same amount P is invested at the same rate R, then interest is directly proportional to time. For 2 years: I₂ = P × R × 2. For 4 years: I₄ = P × R × 4. The ratio I₂ : I₄ = 2PR : 4PR = 2 : 4 = 1 : 2. Option (B) is correct. The answer can be determined - the principal and rate cancel out.

Multiple choice

What total amount would Anushika get at the end of three years if she invests an amount of Rs. 37000 in a scheme which offers compound interest @ 5.5 p.c.p.a.

  1. Rs. 45046.52

  2. Rs. 43446.92

  3. Rs. 43066.52

  4. Rs. 45406.90

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

Amount = Principal × (1 + rate/100)^n = 37000 × (1 + 5.5/100)^3 = 37000 × (1.055)^3 = 37000 × 1.174241... = Rs. 43446.92. Year 1: 37000 × 1.055 = 39035, Year 2: 39035 × 1.055 = 41181.93, Year 3: 41181.93 × 1.055 = 43446.92.

Multiple choice

If the difference of compound interest and simple interest at 12.5% on certain sum of money for third year Rs. 765. Find the sum of money. यदि किसी निश्चित धन पर 12.5% की दर से तीसरे वर्ष के चक्रवृद्धि ब्याज और साधारण ब्याज का अंतर 765 रूपये है, तो मूलधन ज्ञात कीजिये।

  1. 24040 Rs./रू.

  2. 25040 Rs./रू.

  3. 23040 Rs./रू.

  4. 28080 Rs./रू.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The difference between compound interest and simple interest for the 3rd year is given by P × (r/100)^2 × (2 + r/100). Substituting P = 23040 and r = 12.5%: 23040 × (0.125)^2 × 2.125 = 23040 × 0.015625 × 2.125 = 765. Option C matches this calculation.

Multiple choice

A sum of money become 9 times in 24 years at compund interest. Find the time in which it will become 27 time of itself. एक धनराशि चक्रवृद्धि ब्याज की दर से 24 वर्षों में 9 गुनी हो जती है। वह समय बताइये जिसमें वह धनराशि स्वयं की 27 गुनी हो जाए।

  1. 30 year\वर्ष

  2. 48 year\वर्ष

  3. 36 year\वर्ष

  4. 72 year\वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amount becomes 9 times in 24 years, so 3 squarings of (1+r) occur: (1+r)²⁴ = 9. Since 9 = 3², we get (1+r)²⁴ = 3², meaning (1+r)¹² = 3. For 27 times: (1+r)^t = 27 = 3³. Since (1+r)¹² = 3, we need 3 such periods: t = 3 × 12 = 36 years. Option C is correct.

Multiple choice

Simple interest on a certain sum of money for 3 years at 10% per annum is half the compound interest on Rs. 6000 for 2 years at 10% per annum. Find the sum placed on simple interest. 10% प्रतिवर्ष पर 3 वर्षों के लिए एक निश्चित राशि पर साधारण ब्याज 6000 रूपये पर 10% प्रतिवर्ष की दर से 2 वर्ष के चक्रवृद्धि ब्याज का आधा है। साधारण ब्याज पर लगाया गया धन ज्ञात कीजिये।

  1. Rs./रू. 4200

  2. Rs./रू. 2100

  3. Rs./रू. 1050

  4. Rs./रू. 1680
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CI on Rs. 6000 for 2 years at 10%: 6000×(1.1²-1) = 6000×0.21 = Rs. 1260. SI is half of this = Rs. 630. For 3 years at 10%, SI = P×3×0.1 = 0.3P. So 0.3P = 630, P = Rs. 2100.

Multiple choice

The compound interest on Rs 25000 at 12% per anmum for n year is Rs 8241.6 what is the value of n? 25000 रूपयें की राशि पर 12% वार्षिक दर से द वर्षों का चक्रवृद्धि ब्याज 8241.6 है। n का मान क्या होंगा?

  1. 4 year

  2. 3.5 year

  3. 3 year

  4. 2.5 year
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using A = P(1 + r/100)^n: Amount = 25000 + 8241.6 = 33241.6. So 33241.6 = 25000(1.12)^n. 33241.6 ÷ 25000 = 1.32966. Testing n = 2.5: (1.12)^2.5 = 1.3296 (approximately). Therefore n = 2.5 years.

Multiple choice

Find the compound interest on Rs. 18000 in 3 years at 5 % per annum, the interest being compounded yearly? 18000 रुपए पर 3 वर्षो का 5% प्रतिवर्ष की दर से चक्रवृद्धि ब्याज ज्ञात कीजिये,जहां ब्याज की दर वार्षिक है?

  1. Rs. 2837.25

  2. Rs. 2250.25

  3. Rs. 2395.40

  4. Rs. 2295.40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the compound interest formula A = P(1 + r/100)^n, where P = Rs. 18000, r = 5%, n = 3 years. Amount = 18000 × (1.05)^3 = 18000 × 1.157625 = Rs. 20837.25. Therefore, Compound Interest = Amount - Principal = Rs. 20837.25 - Rs. 18000 = Rs. 2837.25.

Multiple choice

Simple interest of first year is Rs. 2700 and the difference of C.I s S.I of 2 year is Rs. 405 find the sum of money. एक वर्ष का साधारण ब्याज 2700 रूपयें है और दो वर्ष के चक्रवृद्धि ब्याज और साधारण ब्याज का अन्तर 405 रूपयें हैं मूलधन ज्ञात कीजिए।

  1. Rs.16000

  2. Rs.19600

  3. Rs. 22000

  4. Rs. 18000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest for first year is Rs. 2700, so annual interest rate on principal P is 2700. For compound interest, the extra interest in year 2 comes from interest on the first year's interest: (2700 × r/100) = 405. Solving gives r = 15%. Then 2700 = P × 15/100 gives P = Rs. 18000. Option A (Rs. 16000) and B (Rs. 19600) result from incorrect rate calculations.