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

Vimal invested a certain amount at simple interest. The total amount sum to Rs. 14760 and Rs. 16140 after 2 years and 3 years respectively. What is the rate of interest at which Vimal invested the amount?

  1. 7.8%

  2. 12.6%

  3. 11.5%

  4. 8.6%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be principal, R be rate. Amount after 2 years = P(1 + 2R/100) = 14760. Amount after 3 years = P(1 + 3R/100) = 16140. Subtracting: P(R/100) = 16140 - 14760 = 1380. So PR/100 = 1380. From first equation: P + 2PR/100 = 14760. P + 2(1380) = 14760. P = 14760 - 2760 = 12000. Then: 12000R/100 = 1380. 120R = 1380. R = 1380/120 = 11.5%. Option C is correct.

Multiple choice

A sum of money when invested for 8 years on simple interest doubles itself. 1/3rd of the amount collected after 8 years is invested again on simple interest at double rate for 3 years. If the amount collected after 3 years is Rs. 21000 then find the sum invested initially.

  1. Rs. 16000

  2. Rs. 20000

  3. Rs. 15000

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

Let principal be P and rate be r%. If P doubles in 8 years at simple interest, then P = (P × r × 8)/100, giving r = 12.5%. After 8 years, amount = 2P. One-third of this (2P/3) is reinvested at 2r = 25% for 3 years. Interest = (2P/3) × 25 × 3/100 = P/2. Total amount = 2P/3 + P/2 = (4P + 3P)/6 = 7P/6 = 21,000, giving P = 18,000.

Multiple choice

The compound interest on a certain sum of money at 21% for 2 years is Rs. 6,961.5. Its simple interest (in Rs.) at the same rate and for the same period is:

  1. Rs. 6,300

  2. Rs. 6,500

  3. Rs. 6,000

  4. Rs. 6,750
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the compound interest formula to find the principal: CI = P[(1 + r/100)^n - 1]. 6961.5 = P[(1.21)^2 - 1] = P[1.4641 - 1] = 0.4641P, so P = 15000. Simple interest = P × R × T / 100 = 15000 × 21 × 2 / 100 = 6300.

Multiple choice

At what rate of interest, compounded annually, should a sum of Rs 10,000 be invested, such that the amount becomes thrice the principal in 3 years? (Round your answer to the nearest integer)

  1. 24%

  2. 42 %

  3. 44%

  4. 62%

  5. 56%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using compound interest formula: A = P(1 + r/100)^t. Given A = 3P, t = 3 years. So 3P = P(1 + r/100)³, meaning (1 + r/100)³ = 3. Therefore 1 + r/100 = ³√3 ≈ 1.442, so r/100 ≈ 0.442, r ≈ 44.2%. Rounded to nearest integer: 44%.

Multiple choice

A borrowed a sum of Rs.1,60,000 from B at 10% per annum simple interest. At the same time he lent the same sum to C at the same time on compounded interest, compounded semi-annually for 2 years. Find the amount (in Rs.) earned by A in the whole transaction.

  1. 4280

  2. 4281

  3. 2481

  4. 2840

  5. 2829
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A pays simple interest: 160000 × 10% × 2 = Rs 32000. A receives compound interest at 10% semi-annually for 2 years (4 periods): 160000[(1 + 0.05)^4 - 1] ≈ 160000 × 0.21550625 = Rs 34481. Profit = 34481 - 32000 = Rs 2481.

Multiple choice

When two equal amounts are deposited for 5 years and 3 years at the rate of 7% and 9% per annum, respectively, the difference of their simple interest is ₹475. Then find the deposited amount. जब दो समान राशि क्रमशः 7% और 9% प्रति वर्ष की दर से 5 वर्ष और 3 वर्ष के लिए जमा की जाती है, तो उनके साधारण ब्याज का अंतर ₹475 है। तो जमा राशि ज्ञात कीजिए।

  1. ₹5,837.5

  2. ₹5,937.5

  3. ₹5,992.5

  4. ₹6,037.5

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

Let principal be P. SI for 5 years at 7% = P * 7 * 5/100 = 0.35P. SI for 3 years at 9% = P * 9 * 3/100 = 0.27P. Difference = 0.35P - 0.27P = 0.08P = 475. So P = 475/0.08 = 5937.5. Option B is correct.

Multiple choice

The compound interest earned after three years and that earned after two years on a certain sum of money, differ by Rs 5880. What is the principal sum of money if the rate of interest is 16.67% p.a? तीन साल बाद अर्जित चक्रवृद्धि ब्याज और एक निश्चित राशि पर दो साल बाद अर्जित ब्याज के बीच अंतर 5880 रुपये है। यदि ब्याज की दर 16.67% प्रति वर्ष है तो मूल राशि क्या है?

  1. Rs. 27432 रु. 27432

  2. Rs. 25920 रु. 25920

  3. Rs. 26780 रु. 26780

  4. Rs. 29870 रु. 29870

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

Rate 16.67% = 1/6. Let principal be P. CI for 2 years = P * (1 + 1/6)^2 - P = P * (49/36 - 1) = 13P/36. CI for 3 years = P * (1 + 1/6)^3 - P = P * (343/216 - 1) = 127P/216. Difference = 127P/216 - 13P/36 = 127P/216 - 78P/216 = 49P/216 = 5880. P = 5880 * 216/49 = 120 * 216 = 25920. Option B is correct.

Multiple choice

A sum lent at simple interest amounts to Rs. 6,240.80 in one year and to Rs. 7,563.20 in 4 years. The sum (in Rs.) and the rate of interest per annum, respectively, are: साधारण ब्याज पर उधार दी गई राशि एक वर्ष में रु. 6,240.80 और 4 साल में रु. 7,563.20 हो जाती है राशि (रुपये में) और प्रति वर्ष ब्याज की दर, क्रमशः हैं:

  1. 6,200, 8.5%

  2. 5,800, 8.5%

  3. 5,800, 7.6%

  4. 6,200, 7.6%

  5. 6,400, 12.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest for 3 years (year 4 minus year 1) = 7,563.20 - 6,240.80 = 1,322.40. Annual interest = 1,322.40/3 = 440.80. Principal = 6,240.80 - 440.80 = 5,800. Rate = (440.80/5,800) × 100 = 7.6% per annum. Option C (5,800, 7.6%) is correct.

Multiple choice

A sum of Rs 12,000 amounts to Rs 20,736 in 3 years at a certain rate percent per annum, interest compounded annually. What will the amount of the same sum be in 2 years at the same rate on compound interest?

  1. Rs15,640

  2. Rs17,820

  3. Rs17,280

  4. Rs14,520
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amount = P(1 + r/100)^t. Given 20736 = 12000(1 + r/100)^3. Therefore (1 + r/100)^3 = 20736/12000 = 1.728. So 1 + r/100 = ∛1.728 = 1.2, giving r = 20%. For 2 years: Amount = 12000(1.2)^2 = 12000 × 1.44 = ₹17,280.

Multiple choice

A sum was put at simple interest at a certain rate for 5 years. Had it been put at 5% higher rate, it would have fetched Rs. 500 more. What is the sum? एक राशि को 5 वर्षों के लिए साधारण ब्याज पर एक निश्चित दर पर रखा गया था। अगर इसे 5% अधिक दर पर लगाया जाता, तो उसे रु 500 अधिक मिलते तो राशि क्या है?

  1. 2700

  2. 2560

  3. 2000

  4. 2400

  5. 1850
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let principal = P, rate = r% per year. Simple interest for 5 years = P × r × 5/100. At rate (r+5)%: interest = P × (r+5) × 5/100. Difference: P × 5 × 5/100 = 500. So: P/4 = 500, giving P = 2000. The sum is Rs. 2000.

Multiple choice

A certain sum amounts to Rs.291600 in 2 years and to Rs.314928 in 3 years on compound interest compounded annually. How much will be the simple interest (in Rs.) on Rs.40,000 at the same rate for 2 years? एक निश्चित राशि सालाना चक्रवृद्धि ब्याज पर 2 साल में 291600 रुपये और 3 साल में 314928 रुपये हो जाती है। 2 वर्ष के लिए समान दर पर 40,000 रुपये पर साधारण ब्याज (रु में) कितना होगा?

  1. 7500

  2. 6400

  3. 8000

  4. 9600

  5. 10400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From the compound interest data, find the rate by dividing the amount after 3 years by amount after 2 years: 314928/291600 = 1.08, so r = 8%. Then simple interest on 40000 for 2 years at 8%: 40000 × 0.08 × 2 = 6400.