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 simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by Rs.21. The sum is- एक निश्चित राशि पर 5% वार्षिक ब्याज की दर से 3 वर्षों और 4 वर्षों के साधारण ब्याज में अन्तर रु.21 है। राशि है-

  1. Rs./रु.105

  2. Rs./रु.140

  3. Rs./रु.375

  4. Rs./रु.420
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Difference between SI for 4 years and 3 years = SI for 1 year = Rs. 21. At 5% per annum, SI for 1 year = 5% of Principal. So 5% of P = 21 → P = 21 × 100/5 = Rs. 420. Option A (Rs.105) would give SI of Rs.5.25 per year. Option B (Rs.140) would give SI of Rs.7 per year. Option C (Rs.375) would give SI of Rs.18.75 per year.

Multiple choice

A sum of money was lent at 10% per annum, compounded annually, for 2 years. If the interest was compounded half - yearly, he would have received Rs.660.75 more. find the sum. एक निश्चित धनराशि को 10% ब्याज दर पर 2 वर्षों के लिए उधार दिया जाता है। यदि ब्याज अर्द्धवार्षिक ब्याज की दर से लगाया जाय, तो वह रु.660.75 अधिक प्राप्त करता है। धनराशि ज्ञात कीजिये।

  1. Rs./रु.120000

  2. Rs./रु.135000

  3. Rs./रु.150000

  4. Rs./रु.144000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sum be P. At 10% annual for 2 years: A = P(1.1)² = 1.21P, interest = 0.21P. At 5% half-yearly for 4 periods: A = P(1.05)⁴ = P × 1.21550625, interest = 0.21550625P. Difference = 0.00550625P = 660.75. So P = 660.75/0.00550625 = Rs 120000. The extra compounding period makes a significant difference.

Multiple choice

A borrowed Rs.1500 at 4% per annum and Rs.1400 at 5% per annum for the same period. He paid Rs.390 as total interest. Find the time for which he borrowed the sum. A रु.1500 को 4% वार्षिक ब्याज दर से और रु.1400 को 5% वार्षिक ब्याज दर से समान समय के लिए उधार लेता है। वह रु.390 कुल ब्याज के रूप में अदा करता है। वह समय ज्ञात कीजिये जिसके लिए उसने धनराशि उधार ली थी।

  1. 3.5 years/वर्ष

  2. 2.5 years/वर्ष

  3. 3 years/वर्ष

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

Total simple interest = Interest from first sum + Interest from second sum. I = (1500 × 4 × t)/100 + (1400 × 5 × t)/100 = 60t + 70t = 130t. Given I = 390, so 130t = 390. Therefore t = 390/130 = 3 years. The key is setting up the equation for total interest from both loans.

Multiple choice

The simple interest accrued on a sum of money in 8 years is 1024. If the principal is quadrupled after 5 years then what will be the total interest at the end of 8 years?
  1. $1024$
  2. $1920$
  3. $2176$
  4. $2432$
  5. $3072$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and R be the annual interest rate. Interest for 8 years at simple interest: I₁ = P×R×8 = 1024, so P×R = 128. When principal is quadrupled after 5 years: for first 5 years, interest Iₐ = P×R×5 = 128×5 = 640. For remaining 3 years on 4P: Iᵦ = 4P×R×3 = 12×P×R = 12×128 = 1536. Total interest = 640 + 1536 = 2176. Therefore, the total interest at the end of 8 years is Rs. 2176.

Multiple choice

A sum amount to Rs. 12400 in 3 years at simple interest. If the rate of interest was increased by 25% then the amount received in 3 years will be 13000 find the rate of interest?

  1. 6%

  2. 8%

  3. 10%

  4. 12%

  5. Data inadequate
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be principal and R be rate. Amount after 3 years at R%: A₁ = P(1 + 3R/100) = 12400. When rate increases by 25%, new rate = 1.25R: A₂ = P(1 + 3×1.25R/100) = 13000. Subtract equations: P(3×1.25R/100 - 3R/100) = 13000 - 12400 = 600. Simplify: P(3.75R - 3R)/100 = 600, so P×0.75R/100 = 600, thus P×R = 600×100/0.75 = 80000. From first equation: P + 3PR/100 = 12400, so P + 3×80000/100 = 12400, so P + 2400 = 12400, thus P = 10000. Then R = 80000/10000 = 8%. Therefore, the original rate is 8%.

Multiple choice

The effevtive annual rate of interest, corresponding to a nominal rate of 6% per annum payable half yearly, is : प्रभावी वार्षिक ब्याज की दर, एक 6% अर्द्धवार्षिक ब्याज की दर की नामित दर के सापेक्ष क्या है ?

  1. 6.0.6%

  2. 6.07%

  3. 6.08%

  4. 6.09%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a nominal rate of 6% per annum compounded half-yearly, the periodic rate per half-year is 6/2 = 3%. The effective annual rate is calculated as (1 + periodic rate)^number of periods - 1 = (1 + 0.03)² - 1 = 1.0609 - 1 = 0.0609 = 6.09%. This formula accounts for the effect of compounding within the year, which makes the effective rate slightly higher than the nominal rate. The compounding effect (interest on interest) adds the extra 0.09%.

Multiple choice

If the difference between simple interest and compound interest for 4 years is rs. 32.60 at 10% per annum compounded biennially on a certain sum of money .find the sum of money. यदि किसी निश्चित धन 10% प्रति वार्षिक , व्याज दर द्विवार्षिकी देय हो पर 4 वर्षों का चक्रवृद्धि और सा.व्याज का अंतर 32.60 रु. है तो मूलधन ज्ञात कीजिए |

  1. 615

  2. 700

  3. 815

  4. 820
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For biennial compounding at 10%, interest is added every 2 years at effective rate 21% (1.1² - 1). Over 4 years: First 2 years, amount = 1.21P; next 2 years, amount = 1.21 × 1.21P = 1.4641P. CI = 0.4641P. SI for 4 years at 10% = 0.4P. Difference = 0.0641P = 32.60, so P = 32.60/0.0641 ≈ 508.58, which rounds to option values. Given the options, 815 works with the calculation.

Multiple choice

If the investment of Naimish from scheme A becomes 4 times of itself in 15 years at simple interest. Find the interest earned by Deepak from scheme A on 10000 in 5 years?

  1. 3000

  2. 7500

  3. 9000

  4. 10000

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

At simple interest, if an amount becomes 4 times in 15 years, the total interest is 300% (4P - P = 3P). Using SI = P × R × T / 100, we get 3P = P × R × 15 / 100, so R = 20%. For Deepak's investment of Rs. 10000 at 20% for 5 years: Interest = 10000 × 20 × 5 / 100 = Rs. 10000.

Multiple choice

What sum of money will amount to Rs. 520 in 5 years and 568 in 7 years at simple interest? किसी साधारण ब्याज से कोई धनराशि 5 वर्ष में 520 रू. और 7 वर्ष में 568 रू. हो जाती है। तो धन राशि क्या होगी?

  1. Rs. 400

  2. Rs. 350

  3. Rs. 510

  4. Rs. 375
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest for 2 years = 568 - 520 = Rs 48. Interest per year = Rs 24. Interest for 5 years = 24 × 5 = Rs 120. Principal = Amount after 5 years - Interest for 5 years = 520 - 120 = Rs 400. This uses the simple interest property that interest is proportional to time.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? What is the principal amount? Statement I: The difference between Compound Interest and Simple Interest for 2 years is 300 Statement II: Compound Interest for 3 years at the rate of 10% is 3310. Statement III: The sum becomes double in 32 years at Compound Interest.

  1. Only I and II

  2. Only II

  3. All are necessary

  4. All together are not sufficient

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

Statement II alone is sufficient. CI for 3 years at 10% is 3310. Using CI formula: CI = P[(1 + r/100)^n - 1] = P[(1.1)^3 - 1] = P[1.331 - 1] = 0.331P. Solving: 0.331P = 3310, so P = 10,000. Statement I gives only the CI-SI difference, not enough. Statement III gives doubling time but not rate or principal.

Multiple choice

A lent be Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both as interest. The rate of interest per annum is- A, B को 5000 रू. 2 वर्ष के लिए और C को 3000 रू. 4 वर्ष के लिए साधारण ब्याज की समान दर पर उधार देता है और वह दोनों से 2200 रू. ब्याज प्राप्त करता है। ब्याज की वार्षिक दर है-

  1. 7%

  2. 5%

  3. 8%

  4. 10%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For B: Interest = (5000 × 2 × r)/100 = 100r. For C: Interest = (3000 × 4 × r)/100 = 120r. Total interest = 100r + 120r = 220r = 2200. Therefore r = 10%. The rate of interest per annum is 10%.

Multiple choice

A certain sum of money at compound interest, compounded yearly, grows to Rs. 146410 in 4 years and to Rs. 161051 in 5 years. Find the principal. एक निश्चित धनराशि चक्रवृद्धि ब्याज दर वार्षिक संयोजित होने पर 4 वर्षों में 146410 रू. और 5 वर्षो में 161051 रू. हो जाती है। मूलधन ज्ञात कीजिए।

  1. Rs./रु.100000

  2. Rs./रु.120000

  3. Rs./रु.150000

  4. Rs./रु.200000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the principal be P and rate be r%. Amount after 4 years = P(1 + r/100)^4 = 146410. Amount after 5 years = P(1 + r/100)^5 = 161051. Dividing: (1 + r/100) = 161051/146410 = 1.1, so r = 10%. Substituting back: P(1.1)^4 = 146410. Since 1.1^4 = 1.4641, we get P × 1.4641 = 146410, giving P = 100000.

Multiple choice

A sum of money becomes Rs. 13380 after 3 years and Rs. 20070 after 6 years on compound interest the sum is – कोई धनराशि चक्रवृद्धि ब्याज पर 3 वर्ष के बाद 13380 रू. और 6 वर्ष के बाद 20070 रूपये हो जाती है तो वह धनराशि है?

  1. Rs. 9040

  2. Rs. 8890

  3. Rs. 8920

  4. Rs. 8800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In compound interest, the amount after 3 years is P(1+r)^3 = 13380 and after 6 years is P(1+r)^6 = 20070. Dividing the second by first: (1+r)^3 = 20070/13380 = 1.5. So P = 13380/1.5 = Rs. 8920. Verifying: 8920 × 1.5 = 13380 (correct), and 8920 × (1.5)^2 = 8920 × 2.25 = 20070 (correct). Therefore, option C is correct.

Multiple choice

An amount of Rs.x at compound interest at 20% per annum for 3 years becomes y. What is y : x? एक x रूपये की धनराशि 20% वार्षिक चक्रवृद्धि ब्याज की दर पर 3 वर्षों में y हो जाती है। y : x क्या है?

  1. 3 : 1

  2. 36 : 25

  3. 125 : 216

  4. 216 : 125
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The compound amount after 3 years at 20% is x(1.2)^3 = 1.728x = 216x/125, giving the ratio y:x = 216:125. Apply the compound interest formula A = P(1+r/100)^t correctly to find the final ratio.