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 compound interest on a certain sum at 2.5% p.a. for 2 years is Rs. 81. Find the sum. एक निश्चित धनराशि पर 2 वर्षों में 2.5.% वार्षिक की दर से चक्रवृद्धि ब्याज 81 रू. है। धनराशि ज्ञात कीजिए।

  1. Rs. 1000

  2. Rs. 1200

  3. Rs. 1500

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

Let sum be P. CI for 2 years at 2.5% = P[(1 + 2.5/100)² - 1] = P[(1.025)² - 1] = P(1.050625 - 1) = 0.050625P = 81. So P = 81/0.050625 = 1600.

Multiple choice

What sum of money lent at 5% p.a. simple interest for 4 years will earn same interest as Rs.2000 earns in 3 years at 4% p.a. of simple interest? किस धनराशि पर 5% वार्षिक ब्याज की दर से 4 वर्ष का साधारण ब्याज, 2000 रू. पर 3 वर्ष में 4%वार्षिक ब्याज की दर से प्राप्त साधारण ब्याज के समान होगा?

  1. Rs.1200

  2. Rs.1500

  3. Rs.1800

  4. Rs.2100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First calculate the reference interest: Rs.2000 at 4% p.a. for 3 years earns SI = 2000 × 4 × 3 / 100 = Rs.240. Let the required sum be P. Then P × 5 × 4 / 100 = 240, which gives 20P/100 = 240, so P = 240 × 5 = Rs.1200. Option B (Rs.1500) would give interest Rs.300. Option C (Rs.1800) would give Rs.360. Option D (Rs.2100) would give Rs.420.

Multiple choice

A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to Rs 250 less than the sum lent. What was the sum lent (in Rs)? एक व्यक्ति किसी निश्चित राशि को 5% की वार्षिक दर से साधारण ब्याज पर उधार देता है तथा 15 वर्षों में संयोजित ब्याज की राशि उधार दी गई राशि से 250 रु. कम है । उधार दी गई राशि (रु. में) कितनी थी?

  1. 1000

  2. 1500

  3. 2400

  4. 3000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sum lent = P. Simple interest after 15 years at 5% = P × 5 × 15/100 = 0.75P. Given: 0.75P = P - 250, so 0.25P = 250, giving P = 1000. Verification: Interest on 1000 for 15 years at 5% = 1000 × 0.05 × 15 = 750, which is indeed 250 less than 1000.

Multiple choice

Find the simple interest on Rs. 1000 for 3 years, if rate of interest for 3 years is 4%, 6% and 7% respectively. 1000 रू. का तीन वर्षों में साधारण ब्याज ज्ञात कीजिए, यदि 3 वर्ष में ब्याज की दर 4%, 6% और 7% है।

  1. 110

  2. 130

  3. 150

  4. 170
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest for each year is calculated separately on the principal. Year 1: Rs. 1000 × 4% = Rs. 40. Year 2: Rs. 1000 × 6% = Rs. 60. Year 3: Rs. 1000 × 7% = Rs. 70. Total simple interest = 40 + 60 + 70 = Rs. 170. The key is that simple interest is always calculated on the original principal, not on accumulated interest.

Multiple choice

In what time Rs.8000 will amount to Rs.9261 at 10% per annum compound interest, when the interest is compunded half-yearly? कितने समय में 8000 रु. की धनराशि 10% वाषिक चक्रवृद्धि ब्याज की दर से 9261 रु. हो जायेगी, जब ब्याज अर्द्धवार्षिक चक्रवृद्धि रूप से उपचयित होता है?

  1. 3(1/2) years/वर्ष

  2. 1(1/2) years/वर्ष

  3. 2(1/2) years/वर्ष

  4. 2 years/वर्ष
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Half-yearly compounding at 10% means 5% per half-year. A = P(1 + r/100)^n gives 9261 = 8000(1.05)^n, so (1.05)^n = 1.157625. Since (1.05)^3 = 1.157625, n = 3 half-years = 1.5 years. Option B is correct.

Multiple choice

A sum of Rs.25000 is lent partly at 8% and remaining at 10% per annum. If the yearly interest on the average is 9.2%, the two parts are 25000 रु. की धनराशि को अंशतः 8% पर और शेष को 10% वार्षिक पर उधार दिया जाता है | यदि वार्षिक ब्याज दर औसत रूप से 9.2% है, दोनों भाग है

  1. Rs./रु.10000, Rs./रु.15000

  2. Rs./रु.12000, Rs./रु.13000

  3. Rs./रु.12500, Rs./रु.12500

  4. Rs./रु.16000, Rs./रु.9000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use allegation method: the ratio of amounts is (10-9.2):(9.2-8) = 0.8:1.2 = 2:3. This means one part is 2/5 of 25000 = Rs.10000 and the other is 3/5 of 25000 = Rs.15000. The allegation method gives the correct mixing ratio when two different rates are combined to produce an average rate.

Multiple choice

The compound interest on a certain sum for second year is Rs. 480 and for the third year is Rs. 576. Find the sum / एक निश्चित धनराशि पर निश्चित ब्याज की दर से दूसरे वर्ष का चक्रवृद्धि ब्याज 480 रू. है और तीसरे वर्ष के लिए 576 रू. है। धनराशि ज्ञात कीजिए?

  1. 1500

  2. 1800

  3. 2000

  4. 2400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The compound interest for successive years forms a geometric progression with common ratio (1 + r/100), where r is the annual rate. Since CI for 2nd year is 480 and for 3rd year is 576, we have 576/480 = 1.2, so the rate is 20%. Using CI for 2nd year = P(1 + r/100)(r/100), we get 480 = P(1.2)(0.2), giving P = 2000.

Multiple choice

If the differences between the compound interest, compounded every six months and the simple interest on a certain sum of money at the rate of 12% per annum for one year is Rs. 432, the sum is- एक निश्चित धनाशि पर एक वर्ष के लिए 12% वार्षिक ब्याज की दर चक्रवृद्धि ब्याज जोकि छमाही देय है और साधारण ब्याज में अन्तर 432 रू. है। धनराशि है-

  1. Rs. 100000

  2. Rs. 900000

  3. Rs. 150000

  4. Rs. 120000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For semi-annual compounding at 12% p.a., rate per 6 months = 6%, and amount = P(1 + 0.06)² = P(1.1236). CI = P(0.1236). SI for 1 year at 12% = P(0.12). Difference = P(0.1236 - 0.12) = P(0.0036) = 432. So P = 432/0.0036 = 120000.

Multiple choice

A principal of Rs.10,000 will amount to (in rupees) after 2 years compounded annually, the rate of interest being 10% per annum during the first year 12% per annum during the second year. एक रु.10000 की धनराशि पर 2 वर्षों में चक्रवृद्धि ब्याज की दर से, यदि ब्याज की दर प्रथम वर्ष 10% वार्षिक और दूसरे वर्ष 12% वार्षिक ब्याज की दर से मिश्रधन (रु. में) होगा ।

  1. Rs./रु.12000

  2. Rs./रु.12320

  3. Rs./रु.12500

  4. Rs./रु.11320
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First year amount = 10000 × 1.10 = 11000. Second year amount = 11000 × 1.12 = 12320. Alternatively: 10000 × (1 + 10/100) × (1 + 12/100) = 10000 × 1.1 × 1.12 = 12320.

Multiple choice

Three amounts x, y and z are such that y is simple interest on x and z is the simple interest on y. If in all the three cases, rate of interest per annum and all the time for which interest is calculated is the same, then find the relation between the x, y and z. तीन राशियों x, y और z ऐसी हैं कि x पर साधारण ब्याज y है और y पर साधारण ब्याज z है | यदि सभी तीनों अवस्थाओं में, प्रति वर्ष ब्याज की दर और सभी समयवधि के लिए गणित की गयी है, समान है, तो x, y और z में सम्बन्ध ज्ञात कीजिये |

  1. xyz = 1

  2. x2 = yz

  3. z = x2y

  4. y2 = xz
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using SI = PRT/100, we have y = xRT/100 and z = yRT/100. Substituting y from the first into the second: z = (xRT/100)(RT/100) = x(RT/100)². Multiplying y² = x²(RT/100)² and comparing with xz gives y² = xz.

Multiple choice

The difference between the CI and SI on a certain sum of money at 10% per annum for 3 years is Rs.620. Find the principal if it is known that the interest is compounded annually. एक निश्चित धनराशि पर 3 वर्षों में 10% वार्षिक ब्याज की दर से चक्रवृद्धि ब्याज और साधारण ब्याज में अन्तर 620 रु. है | मूलधन ज्ञात कीजिये यदि यह पता है कि चक्रवृद्धि ब्याज वार्षिक रूप से उप्चयित है |

  1. 200000

  2. 20000

  3. 10000

  4. 100000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 3 years at 10%, the CI-SI difference formula is P(r/100)²(r/100 + 3). With r = 10, this becomes P(0.1)²(3.1) = 0.031P. Setting 0.031P = 620 gives P = 620/0.031 = 20000.

Multiple choice

If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after यदि 6 वर्ष में साधारण ब्याज मूलधन के 30% के बराबर है, यह मूलधन के बराबर कितने समय के बाद होगा

  1. 20 years/वर्ष

  2. 30 years/वर्ष

  3. 10 years/वर्ष

  4. 22 years/वर्ष
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If SI for 6 years = 30% of principal, then SI for 1 year = 5% of principal. For SI to equal principal (100%), we need 100% / 5% = 20 years. This is a direct proportion problem in simple interest.

Multiple choice

A sum of money becomes 3 times in 5 years at simple interest. In how many years will the same sum become 6 times at the same rate of simple interest? / एक धनराशि 5 वर्ष में साधारण ब्याज की दर से तीन गुना हो जाती है। वही धनराशि कितने वर्षों में साधारण ब्याज की दर से स्वयं का 6 गुना हो जायेगा?

  1. 10 years / वर्ष

  2. 12 years / वर्ष

  3. 12.5 years / वर्ष

  4. 10.5 years / वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the principal to become 3 times in 5 years at simple interest, the interest earned is 2P. Using SI = P×R×T/100: 2P = P×R×5/100 gives R = 40% per annum. To become 6 times, interest needed is 5P. Solving: 5P = P×40×T/100 gives 5 = 2T/5, so T = 12.5 years. The rate remains constant, and we find the time needed for 5 times the principal as interest.

Multiple choice

What is the present worth of Rs.5324 due in 3 years hence at 10% per annum compound interest, interest being compounded annually? 5324 रु. की धनराशि का वर्तमान मूल्य क्या है जोकि यहाँ से 3 वर्ष के बाद 10% वार्षिक चक्रवृद्धि ब्याज की दर से देय है, जबकि ब्याज वार्षिक रूप से उपचयित होता है ?

  1. Rs./रु.5000

  2. Rs./रु.4000

  3. Rs./रु.3600

  4. Rs./रु.3800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find present worth with compound interest, use the formula PV = FV/(1+r)^n where PV is present value, FV is future value (Rs.5324), r is rate (10% or 0.10), and n is time (3 years). PV = 5324/(1.10)^3 = 5324/1.331 = Rs.4000. Verification: 4000 x 1.331 = 5324.