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 an amount of Rs.11250 at the end of the 4 years is Rs.5400. What will be the compound interest at the end of 2 years on the same amount at the same rate of interest? रु.11250 की रकम पर चार वर्ष के अंत में उपचित साधारण ब्याज रु.5400 है | इसी राशि पर इसी दर से दो वर्ष के अंत में चक्रवृद्धि ब्याज कितना उपचित होगा ?

  1. Rs./रु.7454

  2. Rs./रु.2862

  3. Rs./रु.13117

  4. Rs./रु.4284
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Boy got 270 marks and failed by 90, so passing marks = 270 + 90 = 360. This is 45% of total marks, so total marks = 360/0.45 = 800. For girls, passing is 30% of 800 = 0.30 × 800 = 240 marks. Girl got 118, so she needs 240 - 118 = 122 more marks.

Multiple choice

What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and 9 years? एक निश्चित राशि द्वारा समान ब्याज दर पर 6 वर्षों और 9 वर्षों में अर्जित साधारण ब्याज में क्या अनुपात होगा ?

  1. 1 : 3

  2. 1 : 4

  3. 2 : 3

  4. 3 : 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple Interest is directly proportional to time when principal and rate are constant. Using SI = P × R × T / 100, the ratio of interests for 6 years and 9 years equals the ratio of times: 6/9 = 2/3.

Multiple choice

Rs. 1400 amounts to Rs. 2156 in 6 years at a certain rate of interest. If the rate of interest is increased by 1% then Rs. 1400 will amounts to how much ?

  1. 1523

  2. 2130

  3. 2340

  4. 2240

  5. 2140
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For simple interest: 2156-1400=756 is the interest over 6 years. Annual interest = 756÷6=126. Rate = (126×100)÷1400 = 9% per year. If rate increases by 1%, new rate = 10%. New interest = 1400×0.10×6 = 840. New amount = 1400+840=2240. The key is finding the original rate from the first scenario, then applying the increased rate.

Multiple choice

If the compound interest on a certain sum of money for 2 years at 3% per annum is Rs.101.50, then the simple interest on the same sum at the same rate and for the same time will be- यदि एक निश्चित धनराशि पर 2 वर्षों में 3% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज रु.101.50 प्राप्त होता है, तो समान धनराशि पर समान समय के लिए समान ब्याज दर से साधारण ब्याज प्राप्त होगा -

  1. Rs./रु.90.00

  2. Rs./रु.95.50

  3. Rs./रु.100.00

  4. Rs./रु.98.25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI for 2 years at 3% = 101.50. Amount = P(1 + 3/100)² = P(1.0609). CI = 0.0609P = 101.50, so P = 101.50/0.0609 ≈ 1666.67. SI = 1666.67 × 3 × 2/100 = Rs.100.00.

Multiple choice

On a certain principal the compound interest compounded annually for the second year at 10% per annum is Rs.132. The principal is एक निश्चित मूलधन पर 10% चक्रवृद्धि ब्याज की दर से दूसरे वर्ष के लिए चक्रवृद्धि ब्याज रु.132 है | मूलधन है

  1. Rs./रु.1250

  2. Rs./रु.1320

  3. Rs./रु.1000

  4. Rs./रु.1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let principal = P. After 1st year: P × 1.1. Interest for 2nd year = P × 1.1 × 0.1 = 0.11P. Given 0.11P = 132, so P = 132/0.11 = 1200. Verifying: Year 1 interest = 1200 × 0.1 = 120, new principal = 1320. Year 2 interest = 1320 × 0.1 = 132. Option D is correct. Option B (1320) is the amount after 1 year, not the principal.

Multiple choice

If a certain sum of money amounts Rs.18000 in 5 years and Rs.18800 in 7 years at a certain rate of interest. Find the rate of interest.

  1. 2.5%

  2. 4.8%

  3. 5.10%

  4. 6.15%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In simple interest, interest earned each year is constant. Interest earned in 2 years (from year 5 to 7) = 18800 - 18000 = 800, so annual interest = 400. This interest is on the principal for 1 year at rate r: 400 = 18000 × r/100. Therefore r = 400/180 = 2.22%, which rounds to 2.5%. Option A is closest.

Multiple choice

Rahul take a loan of 75000 at a compound interest on 14% rate of interest per annum and lend it to his friend Rahman who returns this amount in three years with simple interest at the rate of 14% per annum. Find the loss or gain of Rahul in the whole transaction. (in rs.)

  1. 4615.8 loss

  2. 4615.8 profit

  3. 3615 profit

  4. 4214 loss

  5. 4214 profit
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rahul pays compound interest: 75000 × (1.14)³ - 75000 = 75000 × 1.481544 - 75000 = 36115.80 interest + principal = 111115.80. He lends at simple interest: 75000 × 14% × 3 = 31500 interest. Received: 75000 + 31500 = 106500. Loss: 111115.80 - 106500 = 4615.80. Compound interest costs more than simple interest over multiple years - Rahul pays 36115.80 but only receives 31500, losing 4615.80. Option A is correct.

Multiple choice

Captain Rahul has taken a loan of 10 lakh from a bank on 6% per annum of simple interest for 10 years. After few years due to a policy for armed forces a discount is given to Captain Rahul on his loan and now he have to pay interest at 4% rate of interest per annum. If he had paid Rs. 14.8 lakh at the end then find after how many years he get the discount?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total interest paid is Rs. 4.8 lakh (14.8 - 10). Let the discount be applied after t years. Interest for first t years at 6%: 10 × 0.06 × t = 0.6t lakh. Interest for remaining (10-t) years at 4%: 10 × 0.04 × (10-t) = 0.4(10-t) = 4 - 0.4t lakh. Setting total equal to 4.8: 0.6t + 4 - 0.4t = 4.8, giving 0.2t = 0.8, so t = 4 years.

Multiple choice

The difference between the simple interest received from two different banks on Rs. 500 for 2 year is Rs. 2.50. The difference between rate of interest per annum is- दोनों बैंकों के प्रतिवर्ष ब्याज दर बैंकों से मिले 500 पर 2 वर्ष के साधारण ब्याज का अन्तर 2.50 रू. है। प्रतिवर्ष ब्याज दर के बीच अन्तर है-

  1. 0.10%

  2. 2.5%

  3. 0.25%

  4. 1%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For simple interest: SI = P × R × T / 100. For two banks with rates R1 and R2: Difference in SI = 500 × R1 × 2 / 100 - 500 × R2 × 2 / 100 = 10 × (R1 - R2) = 2.50. Therefore, R1 - R2 = 2.50 / 10 = 0.25%. The difference in rates is 0.25%, which matches option C.

Multiple choice

Simple interest on a sum of money in 10 years is 1500 at a constant rate of interest. Find simple interest for 10 years at the same rate of interest when for the first 5 years the principal remains the same but for the next 5 years the principal is tripled?
  1. $2000$
  2. $2400$
  3. $2700$
  4. $3000$
  5. $Cannot be determined$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let principal be P and rate be R%. Simple interest for 10 years: P×R×10/100 = 1500, so PR = 15000. For the new scenario: first 5 years interest = P×R×5/100 = 750, next 5 years principal triples to 3P, so interest = 3P×R×5/100 = 2250. Total interest = 750 + 2250 = 3000. This uses the constant rate R throughout.

Multiple choice

A sum of money amounts to Rs.4840 in 2 years and to Rs.5324 in 3 years at compound interest compounded annually. The rate of interest per annum is- एक धनराशि चक्रवृद्धि ब्याज पर 2 वर्षों में रु.4840 और तीन वर्षों में रु.5324 हो जाती है जबकि वार्षिक ब्याज दर चक्रवृद्धि रूप से संयोजित होती है। वार्षिक ब्याज की दर है-

  1. 8%

  2. 9%

  3. 10%

  4. 11%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let amount after 2 years = A = P(1 + r/100)² = 4840. After 3 years = P(1 + r/100)³ = 5324. Dividing: (1 + r/100) = 5324/4840 = 1.1. So r/100 = 0.1, r = 10%. Alternatively: Interest for 3rd year = 5324 - 4840 = Rs.484. This is the interest on Rs.4840 for 1 year. So r = (484/4840) × 100 = 10%.

Multiple choice

Equal sum of money are lent to A and B at 7.5% per annum for a period of 4 years and 5 years respectively. If the difference in interest, paid by them was Rs. 225, the sum lent to each was. समान धनराशि को A और B को 7.5 वार्षिक ब्याज की दर से क्रमशः 4 व 5 वर्ष के लिए उधार दिया जाता है। यदि ब्याजों में अन्तर, जो उनके द्वारा देय था, रू. 225 है। प्रत्येक को उधार दी गई धनराशि है।

  1. Rs. 2500

  2. Rs. 2400

  3. Rs. 3000

  4. Rs. 2800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sum = P. For A (4 years): Interest = P×7.5×4/100 = 0.3P. For B (5 years): Interest = P×7.5×5/100 = 0.375P. Difference = 0.375P - 0.3P = 0.075P. Given 0.075P = 225, so P = 225/0.075 = 3000. The sum lent to each was Rs. 3000.

Multiple choice

A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times of itself at the same rate of interest in- एक निश्चित धनराशि चक्रवृद्धि ब्याज से 5 वर्ष में दोगुनी हो जाती है। यह स्वयं का आठ गुना उसी ब्याज की दर से कितने समय में हो जायेगी-

  1. 10 years/वर्ष

  2. 12 years/वर्ष

  3. 15 years/वर्ष

  4. 20 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If money doubles in 5 years at compound interest, then (1+r)^5 = 2. For eight times: (1+r)^n = 8 = 2^3 = ((1+r)^5)^3 = (1+r)^15. Therefore n = 15 years. The money will become eight times itself in 15 years at the same compound interest rate.