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 ratio of two year C.I. and one year S.I. of certain sum on certain rate of interest is (2.3 : 1). What is the rate of interest?

  1. 20%

  2. 25%

  3. 10%

  4. 30%

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

Let the principal be P and rate be r%. SI for 1 year = Pr/100. CI for 2 years = P[(1 + r/100)² - 1]. The ratio [(1 + r/100)² - 1]/(r/100) = 2.3. Solving: (1 + r/100)² - 1 = 2.3r/100, which gives 1 + 2r/100 + r²/10000 - 1 = 2.3r/100, so 2r/100 + r²/10000 = 2.3r/100, leading to r²/10000 = 0.3r/100, thus r = 30. Option D is correct.

Multiple choice

A sum become 49 times at certain rate of compound interest in 72 year in what time it will become 16807 time at same rate of compound interest ?

  1. 360

  2. 90

  3. 108

  4. 180

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

If a sum becomes 49 times in 72 years at compound interest, and 49 = 7², it means the amount doubles every 36 years (since 72 years gives 7²). We need 16807 = 7⁵. From 7² to 7⁵, we need 3 more doubling periods: 3 × 36 = 108 years. Alternatively: In 72 years, amount multiplies by 7². For 16807 = 7⁵, we need 5 doubling periods of 7. Since 72 years gives 2 periods, each period takes 36 years. For 5 periods: 5 × 36 = 180 years.

Multiple choice

There are two schemes A and B, scheme A gives 12.5% interest rate whereas scheme B gives 21% interest rate. A person invests in them in the ratio of 4:5. After 3 years, the difference between interest from A and interest from B is Rs 2145, calculate the total amount invested ?

  1. Rs.11700

  2. Rs.12480

  3. Rs.13200

  4. Rs.15800

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

Let investments in scheme A and B be 4x and 5x respectively. Simple Interest from A = 4x × 12.5% × 3 = 1.5x. Simple Interest from B = 5x × 21% × 3 = 3.15x. Difference = 3.15x - 1.5x = 1.65x = 2145. So x = 2145/1.65 = 1300. Total investment = 4x + 5x = 9x = 9 × 1300 = Rs. 11700.

Multiple choice

The simple interest accured on an amount of Rs.15500 at the end of three years is Rs. 5580. What would be the compound interest accured on the same amount at the same rate in the same period? (upto two places of decimal)

  1. Rs. 6726.48

  2. Rs. 6276.38

  3. Rs. 6267.83

  4. Rs. 6627.43

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

First find the rate: SI = P×R×T/100, so 5580 = 15500×R×3/100, giving R = 12%. Then CI = P(1 + R/100)^T - P = 15500(1.12)^3 - 15500 = 15500(1.404928) - 15500 = 21776.38 - 15500 = 6276.38. The compound interest is Rs. 6276.38, which matches Option B. The key difference is that CI earns interest on accumulated interest.

Multiple choice

Find the difference between the simple interest and the compound interest on Rs.7500 @ 12% at the end of the three years.

  1. Rs.366.96

  2. Rs.336.96

  3. Rs.366.36

  4. Rs.336.36

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

Simple Interest = P × R × T = 7500 × 0.12 × 3 = Rs. 2700. Compound Interest = P(1 + r)^t - P = 7500(1.12)³ - 7500 = 7500 × 1.404928 - 7500 = Rs. 3036.96. Difference = 3036.96 - 2700 = Rs. 336.96. The key difference is compound interest earns interest on interest.

Multiple choice

Dheeraj invested Rs 35000 in a bank for 1 year at 12% per annum. How much more should Dheeraj need to invest at 10% per annum for that year, so that he can get the same interest amount which he would get when he invests Rs 40000 at 14% per annum for one year?

  1. 10000 Rs

  2. 12500 Rs

  3. 15000 Rs

  4. 14000 Rs

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

Interest on Rs 40000 at 14% = Rs 5600. Interest on Rs 35000 at 12% = Rs 4200. Additional interest needed = Rs 5600 - Rs 4200 = Rs 1400. Let additional amount be P at 10%. Then P × 10% = 1400, so P = 14000.

Multiple choice

The compound interest earned by Rajmohan on a certain amount at the end of two years at the rate of 20% per annum was Rs.4941.2 . What was the total amount after two year ? राजमोहन ने 20% की वार्षिक दर पर दो वर्ष के बाद एक निश्चित धनराशि पर 4941.2 रु. चक्रवृद्धि ब्याज अर्जित किया । तो दो वर्ष बाद का कुल मिश्रधन क्या था ?

  1. Rs./रु.11230

  2. Rs./रु.16117.2

  3. Rs./रु.16171.2

  4. Rs./रु.17161.2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The compound interest for 2 years at 20% is 0.44P (since 1.2² - 1 = 0.44). From CI = 4941.2, we get P = 4941.2/0.44 = 11230. Total amount = Principal + CI = 11230 + 4941.2 = 16171.2.

Multiple choice

Mr. Kapoor took a loan of Rs.10, 000 on simple interest for two years at the rate of 3 p.c.p.a. The total amount that he will be paying as interest in 2 years is 3% of his monthly salary. What is his monthly salary? मि. कपूर 10, 000 रू. का एक कर्ज साधारण ब्याज पर 3 प्रतिशत वार्षिक ब्याज की दर से 2 वर्ष के लिए लेते हैं। कुल धनराशि जो वह ब्याज के रूप में 2 वर्ष में अदा करेंगें वह उनकी मासिक आय का 3% है। उनकी मासिक आय क्या है?

  1. Rs. /रू. 12000

  2. Rs. /रू.16000

  3. Rs. /रू. 20000

  4. Rs. /रू. 30000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

SI = P × R × T / 100 = 10000 × 3 × 2 / 100 = Rs. 600. This equals 3% of monthly salary. So 0.03 × salary = 600, giving salary = Rs. 20,000. Option C is correct. This is a straightforward simple interest calculation.

Multiple choice

The S.I. accrued on a sum of certain principal in 8 years at the rate of x% per year is Rs.6500. What would be the C.I. accrued on that principal at the rate of 8% per year in 2 years, if the value of x is 62.5% more than the given time (in case of simple interest)? किसी निश्चित मूलधन पर 8वर्ष में x% प्रति वर्ष की दर से प्राप्त साधारण ब्याज 6500 रू. है। उस मूलधन पर 8% प्रति वर्ष ब्याज की दर से 2 वर्ष में प्राप्त चक्रवृद्धि ब्याज क्या होगा, यदि x का मान दिए गए समय (साधारण ब्याज की स्थिति में) से 62.5% अधिक है?

  1. Rs. / रू. 1040

  2. Rs. / रू. 1020

  3. Rs. / रू. 1060

  4. Rs. / रू. 1200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

SI = P × x × 8 / 100 = 6500, so P = 81250/x. Given x is 62.5% more than time (8 years), so x = 8 + 0.625×8 = 13%. Then P = 81250/13 = 6250. CI at 8% for 2 years: 6250[(1.08)^2 - 1] = 6250 × 0.1664 = Rs. 1040. Option A is correct.

Multiple choice

What is the rate of interest percent per annum? I. The simple interest of 6 years is 27.5% of principal. II. The simple interest of 10 years is Rs 8420. III. The principal becomes double in 8 years at annual compound interest.

  1. I or III

  2. I and III or II

  3. Any two

  4. Any one

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

Statement I: SI for 6 years = 27.5% of principal, so rate = 27.5/6 = 4.58% per annum. Statement III: Principal doubles in 8 years at CI, which matches the same rate. Statement II gives amount but not principal, so it's insufficient alone. Either I or III can give the answer.

Multiple choice

A man took loan from a bank at the rate of 15% per annum simple interest. After 4.25 years, he had to pay Rs. 8160.What is the principal amount borrowed by him? एक आदमी 15% साधारण ब्याज की दर पर बैंक से कर्ज लेता है। 4.25 वर्ष बाद, उसे इस अवधि के लिए 8160 रुपये का ब्याज भुगतान करना पड़ता है। उसके द्वारा उधार ली गई मूल धनराशि क्या थी?

  1. Rs.12000/12000 रुपये

  2. Rs.12800/12800 रुपये

  3. Rs.20800/20800 रुपये

  4. Rs.14400/14400 रुपये
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple Interest formula: SI = P × R × T / 100. Given SI = Rs. 8160, R = 15%, T = 4.25 years. So 8160 = P × 15 × 4.25 / 100 = P × 63.75 / 100 = P × 0.6375. Therefore P = 8160 / 0.6375 = Rs. 12800. The calculation is straightforward once you set up the SI formula correctly. Option B matches this result.

Multiple choice

What is the difference between the simple interest and compound interest on a certain amount after 3 years? I. Rate of interest is 4% annually. II. The simple interest on the sum after 5 years is Rs. 3000. III. The difference between simple interest and compound interest after 2 years is Rs. 14.

  1. All three together are not sufficient

  2. I and II

  3. I and III

  4. Any two

  5. All three together are sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From I: r=4% annually. From II: SI for 5 years = 3000, so P = 3000×100/(5×4) = 15000. CI-SI for 3 years = PR²(R+300)/(100)³ = 15000×16×304/1000000 = 72.96. The exact formula gives 73, not 72 or 72.8. Statement III gives the difference for 2 years, which doesn't match the calculated value. However, statements I and II together are sufficient to find the answer for 3 years.

Multiple choice

A sum of money becomes Rs. 3600 in 2 years and 5184 in 4 years at certain rate of compound interest per annum. What is the approximate sum of money?

  1. 3000 Rs

  2. 2750 Rs

  3. 2250 Rs

  4. 2600 Rs

  5. 2500 Rs
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Using the compound interest formula A = P(1 + r/100)^n, we have P × (1 + r/100)^2 = 3600 and P × (1 + r/100)^4 = 5184. Dividing gives (1 + r/100)^2 = 5184/3600 = 1.44, so 1 + r/100 = 1.2, meaning r = 20%. Then P = 3600/1.44 = 2500. Checking: 2500 × 1.2^2 = 3600 and 2500 × 1.2^4 = 5184.

Multiple choice

In how much time will a sum of Rs 1600 amount to Rs 1852.20 at 5% per annum compound interest? रू 1600 की एक राशि कितने समय में 5% प्रति वर्ष चक्रवृद्धि ब्याज से रू 1852.20 हो जायेगी?

  1. 3

  2. 2.5

  3. 3.5

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

Using compound interest formula A = P(1 + r/100)^t. For year 3: 1600 × 1.05³ = 1600 × 1.157625 = 1852.20. This matches exactly. For year 2.5, we'd need fractional year calculation, and 3.5 or 4 years would exceed the amount.

Multiple choice

Jaggu lent out some amount of money at 12% simple interest and an equal amount of money at 8% simple interest for 3 years. If his total interest was Rs.10800, what amount was lent out in each case? जग्गू ने कुछ राशि 12% साधारण ब्याज पर और उतनी ही राशि 8% साधारण ब्याज की दर पर 3 वर्षो के लिए उधार दिया। यदि उसे कुल ब्याज 10800 रु. मिला, तो प्रत्येक स्थिति में कितनी राशि उधार दी गई थी?

  1. 18000

  2. 24000

  3. 12000

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

Let amount lent at each rate = x. Total interest = x×12×3/100 + x×8×3/100 = 36x/100 + 24x/100 = 60x/100 = 3x/5 = 10800. So x = 10800×5/3 = 18000. Each amount lent was Rs. 18000.