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

Find the annual installment that will discharge a debt of Rs. 17200 due in 4 years ar 5% per annum simple interest.

  1. Rs. 3500

  2. Rs. 4000

  3. Rs. 3000

  4. Rs. 4500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For simple interest, each installment of Rs. x is paid at end of years 1, 2, 3, 4. Interest on first installment for 3 years, second for 2 years, third for 1 year: Total = x(1 + 1.05 + 1.10 + 1.15) = 17200. Using x = 4000: 4000(1 + 1.05 + 1.10 + 1.15) = 4000 × 4.30 = 17200. Option B is correct.

Multiple choice

Bashant lent a sum of money at the rate of simple interest 4%. If the interest for 8 years is Rs. 340 less than the principal, then what was the principal? बसंत एक धनराशि 4% की साधारण ब्याज की दर से उधार लेता है। यदि 8 वर्ष के लिए ब्याज मूलधन से 340 रू. कम है, तो मूलधन कितना था?

  1. Rs. 500

  2. Rs. 5000

  3. Rs. 400

  4. Rs. 600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest = P × R × T = P × 0.04 × 8 = 0.32P. Given interest is 340 less than principal: 0.32P = P - 340, so 0.68P = 340, P = 340/0.68 = 500.

Multiple choice

What will be the diiference of simple and compound interest on Rs.2880 after three years at the rate of 10% p.a?

  1. Rs. 62

  2. Rs. 91.24

  3. Rs. 67.50

  4. Rs. 89.28
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest = P × R × T = 2880 × 0.10 × 3 = Rs. 864. Compound Interest = P(1 + r)^t - P = 2880(1.1)³ - 2880 = 2880 × 1.331 - 2880 = 3833.28 - 2880 = Rs. 953.28. Difference = 953.28 - 864 = Rs. 89.28. The difference grows each year as compound interest earns interest on interest.

Multiple choice

The compound interest earned by Kanishk on a certain amount at the end of two years at the rate of 8 p.c.p.a. was Rs.1414.40. What was the total amount that Kanishk got back at the end of two years in the form of principal plus interest earned?

  1. Rs.9414.40

  2. Rs.9914.40

  3. Rs.9014.40

  4. Rs.8914.40

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

Compound interest for 2 years at 8%: CI = P[(1 + 8/100)² - 1] = P[1.1664 - 1] = 0.1664P. Given CI = Rs 1414.40, so P = 1414.40/0.1664 = Rs 8500. Total amount = Principal + CI = 8500 + 1414.40 = Rs 9914.40. This matches option B exactly.

Multiple choice

A sum placed at simple interest doubles itself in 12 years. In what time it will become 8 times? साधारण ब्याज पर रखी गयी एक राशि 12 वर्षों में दो गुना हो जाती है। वह कितने समय में स्वयं का 8 गुना हो जाएगी?

  1. 36 years/वर्ष

  2. 48 years/वर्ष

  3. 84 years/वर्ष

  4. 96 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If sum doubles in 12 years, simple interest equals principal in 12 years. So rate = 100/12% per year. To become 8 times, interest needed = 7 times principal. At rate (100/12)% per year, time needed = (7 × 100) / (100/12) = 7 × 12 = 84 years. Formula: Time = (RequiredInterest × PrincipalTime) / Principal

Multiple choice

Find the compound interest on a sum of Rs. 4880 at 15% rate of interest for a time period of 3 years. 4880 रूपये मूलधन पर 3 वर्ष का 15% ब्याज दर पर चक्रवृद्धि ब्याज ज्ञात कीजिए।

  1. Rs. 2484.75

  2. Rs. 2541.75

  3. Rs. 2692.125

  4. Rs. 2424.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Compound Interest formula: A = P(1 + r/100)^n. P = 4880, r = 15%, n = 3. A = 4880 × (1.15)^3 = 4880 × 1.520875 = 7421.875. CI = A - P = 7421.875 - 4880 = 2541.75. The compound interest for 3 years at 15% on Rs. 4880 is Rs. 2541.75.

Multiple choice

Rs. 10408 is divided between Aastha and Naimish so that the amount that Aastha receives in 4 years is the same as that Namish receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Aastha's share is -

  1. Rs. 5000

  2. Rs. 5408

  3. Rs. 6080

  4. Rs. 4328

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

Let Aastha's share be x. Then Naimish gets 10408-x. Aastha's amount after 4 years = x(1.04)^4. Naimish's amount after 6 years = (10408-x)(1.04)^6. Equating: x(1.04)^4 = (10408-x)(1.04)^6. This simplifies to x = (10408-x)(1.04)^2. Solving: x ≈ 5408. At 4% compound interest, Aastha needs about Rs. 5408 initially to equal Naimish's amount in 2 fewer years.

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and find which information is/are necessary to answer. For what time the simple interest is Rs. 500? I. The compound interest on the same sum for two years is 484. II. Rate of interest is 5%. III. The difference between compound interest and simple interest on that sum for 2 years is Rs. 41.

  1. All three together are sufficient

  2. I and (II or III)

  3. I and III together

  4. II and (I or III)

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

Statement II: Rate = 5%. Statement III: CI - SI for 2 years = Rs. 41. For rate r, the difference is P*r²/100². So P*(5)²/10000 = 41, giving P = 16400. With P and rate, time for SI=500 is t = 500*100/(16400*5) = 50000/82000 = 50/82 years. Statement I gives CI for 2 years = 484, which can verify P but II+III or II+I are sufficient. Option D (II and I or III) is correct.

Multiple choice

Astha invested a certain amount at the rate of 19 p.c.p.a. for 15 years and obtained simple interest of 27075. If the same amount is invested at the same rate of interest for 2 years, what will be the compound interest at the end of 2 years?

  1. Rs. 3952.95

  2. Rs. 3750.95

  3. Rs. 3255.95

  4. Rs. 4452.95

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

First find the principal from SI: SI = P×R×T/100, so 27075 = P×19×15/100, giving P = (27075×100)/(19×15) = 2707500/285 = 9500. Now calculate CI for 2 years at 19%: CI = P[(1 + R/100)^T - 1] = 9500[(1 + 19/100)^2 - 1] = 9500[(1.19)^2 - 1] = 9500[1.4161 - 1] = 9500×0.4161 = 3952.95. This matches option A.

Multiple choice

A man loses Rs. 45.50 yearly when the annual rate of interest falls from 12% to 10.5%. What is his capital? (in Rupees) एक आदमी को 45.50 रू. वार्षिक की हानि होती है जब ब्याज दर 12% से 10.5% हो जाता है, तो उसकी राशि क्या है? (रू. में)

  1. Rs. 3000

  2. Rs. 3033

  3. Rs. 3500

  4. Rs. 4500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Annual loss = Capital × (rate₁ - rate₂). Here 45.50 = P × (12% - 10.5%) = P × 1.5%. So P = 45.50/0.015 = Rs. 3033.33. The question has rounding/approximation issue - exact answer should be Rs. 3033.33, but option B is Rs. 3033. This tests simple interest rate difference applied to principal.

Multiple choice

What is the compound interest on Rs. 10,000 for 9 months at 20% per annum? (interest being compounded quarterly) 20% वार्षिक दर से 10,000 रू. का 9 माह में चक्रवृद्धि ब्याज क्या होगा? (जब ब्याज तिमाही संयोजित है)

  1. Rs. 1576.25

  2. Rs. 1428.25

  3. Rs. 1500.75

  4. Rs. 1750.50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal = Rs. 10,000, Rate = 20% p.a., Time = 9 months, Quarterly compounding (4 times per year). Rate per quarter = 20/4 = 5%, Number of quarters = 9/3 = 3. Amount = 10000(1+5/100)³ = 10000(1.05)³ = 10000×1.157625 = Rs. 11,576.25. CI = Amount - Principal = 11576.25 - 10000 = Rs. 1,576.25. This tests compound interest with non-annual compounding periods.

Multiple choice

A sum of money at simple interest amount to Rs. 815 in 3 years and to Rs. 854 in 4 years.The sum is - एक धनराशि साधारण ब्याज की दर से 3 वर्षो में 815 रू. और 4 वर्षों में 854 रू. हो जाती है तो धनराशि क्या है?

  1. Rs. 700

  2. Rs. 698

  3. Rs. 690

  4. Rs. 650
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interest for 1 year = 854 - 815 = Rs. 39 (simple interest is constant). Principal for 3 years = 815 - 3*39 = 815 - 117 = Rs. 698. Verification: 698 + 4*39 = 698 + 156 = Rs. 854 ✓. Option B correct.

Multiple choice

Divide Rs.1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum. What is the smaller part?

  1. 525

  2. 625

  3. 676

  4. 484

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

Let A and B be the initial amounts. After compound interest: A(1.04)^7 = B(1.04)^9. This gives A = B(1.04)^2 = 1.0816B. Since A + B = 1301, we get 2.0816B = 1301, so B = 625 (the smaller share). A = 676 is the larger part.

Multiple choice

The simple interest on a sum of money will be Rs. 600 after 10 years. If the principal is tripled after 5 years, what will be total interest at the end of the tenth year? एक धनराशि पर 10 वर्ष के बाद साधारण ब्याज 600 रू. है। यदि मूलधन को 5 वर्ष के बाद तिगुना कर दिया जाये तो 10 वें वर्ष की समाप्ति पर कुल ब्याज क्या होगा?

  1. Rs. 1200

  2. Rs. 900

  3. Rs. 950

  4. Rs. 1250
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let principal = P and rate = r%. Simple interest for 10 years on P is Rs.600, so (P × r × 10)/100 = 600, meaning Pr = 6000. For first 5 years: interest = (P × r × 5)/100 = 3000/100 = Rs.300. Principal triples after 5 years, so new principal = 3P. Next 5 years interest = (3P × r × 5)/100 = 15 × (Pr)/100 = 15 × 6000/100 = Rs.900. Total interest = 300 + 900 = Rs.1200. Option A is correct.