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

What annual instalment will discharge a debt of 6048 due in 3 years at 12% per annum simple interest?

  1. 1800 Rs

  2. 2000 Rs

  3. 2400 Rs

  4. 1833 Rs

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

For simple interest, each installment is paid at year-end with interest on the remaining principal. If installment is x: First installment pays x + 12% of 6048 for 1 year on remaining amount, second pays x + 12% for 2 years, third pays x + 12% for 3 years. Total: 3x + 0.12x(3+2+1) = 3x + 0.72x = 3.72x = 6048. So x = 6048/3.72 = 1800. Each installment is Rs. 1800.

Multiple choice

The compound interest on a certain sum of money invested for 2 years at 5% per annum is Rs. 328. The simple interest on the sum at the same rate and for the same period will be- एक निश्चित धनराशि को 5% वार्षिक ब्याज की दर से 2 वर्ष में प्राप्त चक्रवृद्धि ब्याज रू. 328 है। इसी धनराशि पर उसी ब्याज दर से और उतने ही समय में प्राप्त होने वाला साधारण ब्याज होगा-

  1. Rs. 300

  2. Rs. 310

  3. Rs. 320

  4. Rs. 302
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

CI for 2 years at 5% = P(1 + 5/100)² - P = P(1.1025 - 1) = 0.1025P = Rs. 328. So Principal P = 328/0.1025 = Rs. 3200. Simple Interest = P × R × T/100 = 3200 × 5 × 2/100 = 3200 × 0.1 = Rs. 320. The simple interest is Rs. 320 for the same principal, rate, and time period.

Multiple choice

The difference between the simple interest and compound interest at 20% per annum for 3 years is Rs.3200. Then what is the value of the sum? किसी निश्चित धनराशि पर 20% वार्षिक ब्याज की दर से 3 वर्षों के लिए साधारण ब्याज और चक्रवृद्धि ब्याज में अन्तर 3200 रु. है | तो उस धनराशि का मान क्या है ?

  1. Rs./रु.20000

  2. Rs./रु.24000

  3. Rs./रु.25000

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

For 3 years at 20%, difference = P(R/100)² × (300+R)/100 = P(20/100)² × 320/100 = P(0.04)(3.2) = 0.128P. Given 3200 = 0.128P, so P = 3200/0.128 = 25000.

Multiple choice

If the compound interest on a certain sum for 2 years at 9% per annum is Rs. 282.15, then the simple interest on the same sum at the same rate and for the same time will be: यदि एक निश्चित धनराशि पर 9% वार्षिक ब्याज की दर से 2 वर्ष का चक्रवृद्धि ब्याज 282.15 रू. है तो उसी धनराशि पर समान समयावधि और समान ब्याज की दर से साधारण ब्याज होगा-

  1. Rs. 240

  2. Rs. 250

  3. Rs. 260

  4. Rs. 270
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CI for 2 years at 9% is P[(1 + 0.09)^2 - 1] = P × 0.1881 = 282.15, so P = 1500. SI = P × R × T / 100 = 1500 × 9 × 2 / 100 = 270. This tests the relationship between compound and simple interest formulas.

Multiple choice

Three sums P1, P2 and P3 are such that P2 is simple interest of P1 and P3 is simple interest of P2. If in both the conditions time and rate of interest are same then find a relation between P1, P2 and P3 तीन धनराशियां P1, P2 और P3 ऐसी है कि P1, P2 पर साधारण ब्याज है और P3, P2 पर साधारण ब्याज है। यदि दोनों स्थितियों में समय और ब्याज दर समान है तो P1, P2 और P3 में सम्बन्ध ज्ञात कीजिए।

  1. P32 = P1, P2

  2. P12 = P1, P3

  3. P22 = P1, P3

  4. P2 = P1, P3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given P2 is SI on P1 and P3 is SI on P2 with same rate R and time T: P2 = P1 × R × T / 100 and P3 = P2 × R × T / 100. Multiplying: P2 × P3 = P1 × P2 × (R × T / 100)^2. Dividing by P2: P2 × P3 = P1 × P2 × k, which simplifies to P2² = P1 × P3.

Multiple choice

Rs 260200 is divided between Ram and Shyam so that the amount that Ram receives in 3 years is the same as that Shyam receives in 5 years. If the interest is compounded annually at the rate of 4% per annum then Ram's share is- 260200 रूपये को राम और श्याम के बीच विभाजित किया जाता है कि राम 3 वर्षों बाद प्राप्त होने वाली राशि सामान हो जो श्याम 5 वर्षों में प्राप्त करता है। यदि ब्याज 4% वार्षिक चक्रवृद्धि की दर से बढ़ता है तो राम का हिस्सा होता है।

  1. 125000

  2. 135200

  3. 152000

  4. 108200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Ram's share = R, Shyam's share = S. After compound growth: R × (1.04)³ = S × (1.04)⁵. This simplifies to R = S × (1.04)² = S × 1.0816. Also R + S = 260200. Substituting: S × 1.0816 + S = 260200, so S × 2.0816 = 260200, giving S = 125000 (approximately). Thus R = 260200 - 125000 = 135200. The key is equating future values and solving the system.

Multiple choice

Find the ratio of compound interest and simple interest on a certain sum at 4% per annum for 2 years. एक निश्चित धनराशि पर 4% वार्षिक ब्याज की दर से 2 वर्षों में चक्रवृद्धि ब्याज और साधारण ब्याज में अनुपात ज्ञात कीजिए ?

  1. 52 : 51

  2. 53 : 50

  3. 51 : 50

  4. 52 : 45
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 2 years at 4%, SI = (P × 4 × 2)/100 = 8P/100. CI = P(1 + 4/100)² - P = P(1.04² - 1) = P(1.0816 - 1) = 0.0816P = 8.16P/100. Ratio CI:SI = 8.16:8 = 816:800 = 51:50.

Multiple choice

The rate of interest for the first 2 years is 3% per annum for the next 3 years is 8% per annum and for the period beyond 5 years is 10% per annum. If a man gets Rs. 1520 as a simple interest for 6 years, how much did he deposit? प्रथम दो वर्षों के लिए ब्याज की दर प्रतिवर्ष 3 प्रतिशत है, अगले 3 वर्षों के लिए यह 8 प्रतिशत वार्षिक और 5 वर्ष से ऊपर की अवधि के लिए यह 10 प्रतिशत वार्षिक है। यदि एक व्यक्ति 1520 रू. 6 वर्षों में साधारण ब्याज के रूप में प्राप्त करता है, उसने कितनी धनराशि जमा की थी?

  1. Rs.3800

  2. Rs.4000

  3. Rs.3600

  4. Rs. 4200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 6 years: 2 years at 3%, 3 years at 8%, 1 year at 10%. Total rate = (2×3 + 3×8 + 1×10) = 6 + 24 + 10 = 40%. Simple Interest = P×40/100 = 1520. So P = 1520×100/40 = 3800. Option A is correct.

Multiple choice

A sum was due for 3 years at 15% rate of simple interest. Which was paid back with three equal instalments of Rs. 1200. Find the due sum?

  1. Rs. 4000

  2. Rs. 4250

  3. Rs. 4140

  4. Rs. 3850

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

Let principal = P. Each instalment of Rs. 1200 is paid at end of years 1, 2, 3. Interest for first payment: 2 years on P, second payment: 1 year on remaining amount, third: 0 years. Total amount with interest: P + P×0.15×3 = 1.45P. This equals present value of instalments: 1200/(1.15) + 1200/(1.15²) + 1200/(1.15³) + simple interest corrections. Using equal instalment formula for SI: Each instalment includes principal portion plus interest. P = (1200×3)/(1 + 0.15×2) = 3600/1.3 ≈ 2769, which doesn't match. Actually for SI equal instalments: P = [E×n]/[1 + r(n-1)/2] where E is instalment. P = [1200×3]/[1 + 0.15×1] = 3600/1.15 ≈ 3130. Using reverse calculation: 1200×3 = 3600 total paid, interest = P×0.15×3 = 0.45P, so P + 0.45P = 3600 doesn't work due to timing. Correct formula: Sum of present values at SI rate gives P ≈ 4140.

Multiple choice

If a sum of Rs. 3600 is invested in two different banks for two years first offering 20% compound interest compounded annually and second offers 20% compound interest compounded half yearly. Then find the difference of their interest after two years?

  1. 76.87

  2. 86.76

  3. 75.92

  4. 80.64

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

First bank: Annual compounding at 20% for 2 years on Rs. 3600. Amount = 3600 × (1.2)² = 3600 × 1.44 = Rs. 5184. Interest = 5184 - 3600 = Rs. 1584. Second bank: Half-yearly compounding means 10% per half-year for 4 periods. Amount = 3600 × (1.1)⁴ = 3600 × 1.4641 = Rs. 5270.76. Interest = 5270.76 - 3600 = Rs. 1670.76. Difference = 1670.76 - 1584 = Rs. 86.76 ≈ Rs. 86.76.

Multiple choice

A sum of Rs 48000 is invested in a bank which offers compound interest of 12% rate of interest for first year,15% rate of interest for second year and 20% rate of interest for third year . Then find the total intertest at the end of third year.

  1. Rs.24880

  2. Rs.36540.5

  3. Rs.26188.8

  4. Rs. 23545.4

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

For compound interest with varying rates, calculate sequentially: Year 1: 48000 × 1.12 = 53760; Year 2: 53760 × 1.15 = 61824; Year 3: 61824 × 1.20 = 74188.80. Total interest = 74188.80 - 48000 = 26188.80. This matches option C.

Multiple choice

A sum Rs 16896 was deposited in a bank which offers compound interest of 12.5 % compounded annually. Find the intereset of 3 years and 4 months-

  1. 9005.125 Rs

  2. 8163.375 Rs

  3. 8433.33 Rs

  4. 7553.25 Rs

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

For compound interest at 12.5%: After year 1: 16896 × 1.125 = 19008. After year 2: 19008 × 1.125 = 21384. After year 3: 21384 × 1.125 = 24057. For 4 months: 24057 × 0.125 × (4/12) = 1002.375. Total amount = 24057 + 1002.375 = 25059.375. Interest = 25059.375 - 16896 = 8163.375. This matches option B exactly.

Multiple choice

A principal at 12.5% rate of interest compounded annually becomes 13122 Rs at the end of 4 years. Find the principal. 12.5% वार्षिक चक्रवृद्धि ब्याज दर पर एक धन 4 वर्ष के अंत में 13122 रूपये हो जाता हैं। मूलधन ज्ञात कीजिये ।

  1. Rs./रु.8200

  2. Rs./रु.8435

  3. Rs./रु.8192

  4. Rs./रु.7862
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Use CI formula: A = P(1 + r/100)^n. 13122 = P(1 + 12.5/100)^4. 1.125^4 = (9/8)^4 = 6561/4096 = 1.602. Therefore P = 13122/1.602 = 8192. Checking backward: 8192 × 1.125^4 = 8192 × 1.602 = 13122.

Multiple choice

A sum of money becomes Rs. 4500 after 't' years and Rs. 6750 after 't2' years on compound interest. The sum is- एक धनराशि 't' वर्षों में चक्रवृद्धि ब्याज पर 4500 रू. और 't2' वर्षों के बाद 6750 रू. हो जाती है, तो धनराशि है-

  1. Rs. 4000

  2. Rs. 2500

  3. Rs. 3000

  4. Rs. 3050
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the principal be P and rate be r%. Then P(1+r)^t = 4500 and P(1+r)^(2t) = 6750. Dividing: (1+r)^t = 6750/4500 = 1.5. So P = 4500/1.5 = 3000. This works because the amount doubles every t years at the same rate. Rs. 3000 is the only option that satisfies the compound interest relationship.