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

There is 60% increase in an amount in 6 year at simple interest. What will be the compound interest on Rs.24000 after 3 years at the same rate of interest? साधारण ब्याज पर एक राशि में 6 वर्ष में 60% की वृद्धि हुई है। उसी ब्याज दर पर 3 वर्ष के बाद 24000 रुपये पर चक्रवृद्धि ब्याज क्या होगा?

  1. Rs./रु.4320

  2. Rs./रु.6240

  3. Rs./रु.7944

  4. Rs./रु.12480
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

60% increase in 6 years at SI means rate = 60/6 = 10% per annum. For CI on Rs.24000 for 3 years at 10%: Amount = 24000 × (1.1)^3 = 24000 × 1.331 = Rs.31944. CI = 31944 - 24000 = Rs.7944. The key is converting the SI information to find the rate first.

Multiple choice

Ajay borrowed Rs.28000 at 10% p.a. He repaid Rs.x at the end of the first year. What amount should he pay at the end of the second year to completely discharge the loan, compound interest being reckoned annually? x has the value such that the borrowed sum is 175% of x. अजय ने 28000 रुपये 10% वार्षिक ब्याज दर पर उधार लिया उसने पहले वर्ष के अंत में x रुपये का भुगतान किया। ऋण को पूरी तरह से निर्वहन करने के लिए दूसरे वर्ष के अंत में उसे कितनी रकम देनी चाहिए, यदि ब्याज चक्रवृद्धि रूप से संयोजित होता? x का मान ऐसा है कि यह उधार राशि , x का 175% है।

  1. Rs.16280

  2. Rs.16440

  3. Rs.12640

  4. Rs.16420
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given borrowed sum = 28000, which is 175% of x, so x = 28000/1.75 = 16000. After year 1: Amount = 28000(1.1) = 30800. Repayment of 16000 leaves 14800. After year 2: 14800(1.1) = 16280. This is the final payment needed. The compound interest formula A = P(1+r)^n is applied sequentially with the repayment.

Multiple choice

A sum of money was invested for T years in Scheme A offering simple interest. The amount received after 'T' years was twice the sum of money invested in the scheme A. What will be the amount received from Scheme A, when a sum of Rs.5450 is invested for '2T' years? एक राशि को स्कीम A में साधारण ब्याज पर T वर्ष के लिए निवेश किया गया । 'T' वर्षों के बाद प्राप्त धनराशि योजना A में निवेश किए गए धन की दोगुनी राशि थी। योजना A से प्राप्त राशि क्या होगी, जब '2 T' वर्षों के लिए 5450 रुपये का निवेश किया जाएगा?

  1. Rs.16290

  2. Rs.15500

  3. Rs.16350

  4. Rs.16500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Under simple interest, if amount becomes twice the principal in T years, then interest = principal, so rate r = 100/T %. For 2T years at same rate, interest = P × r × 2T/100 = P × (100/T) × 2T/100 = 2P. Amount = P + 2P = 3P. For principal Rs. 5450, amount = 3 × 5450 = Rs. 16350.

Multiple choice

A sum of money amounts to Rs.10962 after 5 years and Rs.13003.2 after 8 years at the same rate of simple interest. What is the amount of compound interest at the same rate of interest and on the same sum of money? (nearest value)

  1. Rs.2220

  2. Rs.2230

  3. Rs.2320

  4. Rs.2200

  5. Rs.2222
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For simple interest: Amount after 5 years = P + SI = P + P×R×5/100 = P(1 + 5R/100) = 10962. After 8 years: P(1 + 8R/100) = 13003.2. Difference: P(3R/100) = 13003.2 - 10962 = 2041.2. So PR = 2041.2 × 100/3 = 68040. From 5 year equation: P + 5 × 68040/100 = P + 3402 = 10962, so P = 7560, R = 9%. CI for same principal at 9% for appropriate time = 7560(1.09)^n - 7560. Assuming 8 years: CI = 7560 × 1.99256 - 7560 ≈ 15064 - 7560 = 7504. But answers are around 2200. Let me reconsider - maybe 3 years CI? For 3 years: 7560(1.09)³ - 7560 = 9799 - 7560 = 2239. So approximately 2230, which matches option B.

Multiple choice

If the simple interest on a certain sum of money be Rs.303.60 for 3 years at 4% per annum. What will be the compound interest on the same sum of money and same time and rate? (upto two decimal points)

  1. Rs.310.80

  2. Rs.421.70

  3. Rs.315.90

  4. Rs.350.70

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

Simple Interest: 303.60 = P×3×4/100, so P = 30360/12 = Rs. 2530. Compound Interest for 3 years at 4%: Amount = 2530(1.04)^3 = 2530×1.124864 = Rs. 2845.90. CI = 2845.90 - 2530 = Rs. 315.90. Answer C is correct.

Multiple choice

A certain sum was put on simple interest at 20% per annum for 2 years. The amount received after 2 years put on compound interest 12% per annum for 2 more years. If the amount received at the end of 4 years is Rs.43904, then find the amount invested at starting. एक निश्चित राशि का दो वर्षों के लिए 20% वार्षिक साधारण ब्याज दर पर रखा जाता है । 2 वर्षों के बाद प्राप्त राशि को 12% वार्षिक चक्रवृद्धि ब्याज दर पर 2 और वर्षों के लिए रखा जाता है । यदि 4 वर्ष के अतं में प्राप्त राशि रु.43904 है, तो प्रारम्भ में कितनी राशि निवश की गई थी?

  1. Rs.20000

  2. Rs.25000

  3. Rs.30000

  4. Rs.40000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let principal be P. After 2 years at 20% SI: P(1 + 0.20×2) = 1.4P. Next 2 years at 12% CI: 1.4P(1.12)² = 1.4P × 1.2544 = 1.75616P. Given 1.75616P = 43904, so P = 43904/1.75616 ≈ 25000. The calculation uses SI formula A = P(1 + rt) and CI formula A = P(1 + r)ⁿ.

Multiple choice

The difference between the simple and the compound interest compounded every six months at the rate of 20 per cent per annum at the end of 1 1 2 years is Rs.248. What is the sum? 20 प्रतिशत वार्षिक ब्याज की दर से 1 1 2 वर्षों के अंत में साधारण ब्याज तथा चक्रवृद्धि ब्याज के बीच अंतर रु.248 है, यदि ब्याज प्रत्येक छः माह में संयोजित होता है । राशि क्या है ?

  1. Rs.10000

  2. Rs.6000

  3. Rs.12000

  4. Rs.8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For half-yearly compounding, rate = 10% per period for 3 periods. CI factor = 1.1³ = 1.331. SI for 1.5 years at 20% = 1 + 0.2×1.5 = 1.3. Difference: 1.331P - 1.3P = 0.031P = 248. So P = 248/0.031 = 8000. Key insight: CI compounded half-yearly means rate/2 for 2×time periods.

Multiple choice

What will be the compound interest on an amount of Rs.5500 at the rate of 3% per annum after 2 years? रू. 5500 की राशि पर 3% प्रति वर्ष की दर से 2 वर्ष बाद चक्रवृद्धि ब्याज क्या होगा?

  1. Rs.334.95

  2. Rs.339.95

  3. Rs.354.95

  4. Rs.358.95
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound Interest = P[(1 + r/100)^n - 1]. For P=5500, r=3%, n=2: CI = 5500[(1.03)² - 1] = 5500[1.0609 - 1] = 5500 × 0.0609 = Rs.334.95.

Multiple choice

A man gave 50% of his saving of Rs. 84100 to his wife and divided the remaining sum among his two sons A and B of 15 years 13 years of age respectively. he divided it in such a way that each of his sons, when they attain the age of 18 years would receive the same amount at 5% compound interest per annum. The Share of B was :

  1. 20000

  2. 20050

  3. 22000

  4. 22050

  5. 25000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After giving 50% to wife, remaining amount = Rs. 42050. Son A (15 years) gets amount P_A, son B (13 years) gets amount P_B. A invests for 3 years (until 18), B invests for 5 years (until 18). At 5% CI: P_A(1.05)^3 = P_B(1.05)^5. Solving: P_A/P_B = (1.05)^5/(1.05)^3 = (1.05)^2 = 1.1025. Also P_A + P_B = 42050. Substituting: 1.1025P_B + P_B = 42050, so 2.1025P_B = 42050, giving P_B ≈ Rs. 20000.

Multiple choice

A man deposited a total amount of Rs. 25300 with a bank in two different schemes at 20% p.a. interest being compounded annually . As per the schemes, he gets the same amount after 4 years on the first deposit as he gets after 3 years on the second deposit. How much money did he deposit for 3 years?

  1. Rs.12,000

  2. Rs.15,450

  3. Rs.16,620

  4. Rs.14,440

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

Let first deposit be x and second be y. Total: x + y = 25300. After 4 years at 20% CI: x(1.2)⁴ = x × 2.0736. After 3 years at 20% CI: y(1.2)³ = y × 1.728. These amounts are equal: 2.0736x = 1.728y → y = 1.2x. Substituting: x + 1.2x = 25300 → 2.2x = 25300 → x = 11500. So y = 25300 - 11500 = 13800. Checking: 11500 × 2.0736 = 23846.4 and 13800 × 1.728 = 23846.4. The 3-year deposit is Rs. 13800, which matches none of A-D. Option E (None of these) is correct.

Multiple choice

The difference between the interest received by Anil and Ravi is Rs 120. When they invest Rs 2000 each for 3 years what is the difference in the rate of interest? अनिल और रवि द्वारा प्राप्त ब्याज के बीच अंतर 120 रुपये है, जब वे 3 वर्ष के लिए 2000 रुपये प्रत्येक निवेश करते हैं तो ब्याज दर में क्या अंतर है?

  1. 2%

  2. 7%

  3. 4%

  4. 6%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Difference in simple interest = P*R1*T/100 - P*R2*T/100 = P*T*(R1-R2)/100. Given: 2000*3*(r1-r2)/100 = 120. So 60*(r1-r2) = 120, hence r1-r2 = 2%. The principal and time cancel out in the difference.

Multiple choice

The simple interest accrued on a sum of certain principal is Rs. 2000 in 5 years at the rate of 4 p.c.p.a. What would be the compound interest accrued on same principal at the same rate in two years? एक निश्चित मूलधन पर 4 प्रतिशत वार्षिक ब्याज की दर से 5 वर्ष में अर्जित साधारण ब्याज 2000 रुपये है। दो वर्ष में समान मूलधन पर समान दर पर उपजित चक्रवृद्धि ब्याज क्या होगा?

  1. Rs./रुपये 725

  2. Rs./रुपये 816

  3. Rs./रुपये 600

  4. Rs./रुपये 520
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From SI = P×R×T/100, we get 2000 = P×4×5/100, so P = 10000. For CI in 2 years at 4%, use formula CI = P[(1 + R/100)^2 - 1] = 10000[(1.04)^2 - 1] = 10000[1.0816 - 1] = 816. The key is finding principal from SI first, then applying CI formula.

Multiple choice

The simple interest accrued on a sum of certain principal in 8 yr. at the rate of 13% per year is 6500. What would be the compound interest accrued on that principal at the rate of 8% per year in 2 yr.?

  1. 1040

  2. 1020

  3. 1060

  4. 1200

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

From SI formula, P = (6500 × 100)/(13 × 8) = 6250. CI for 2 years at 8% = 6250 × [(1.08)² - 1] = 6250 × 0.1664 = 1040. The key is finding principal from the simple interest information first.