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 simple interest on a certain sum for 3 years at 12% p.a. is Rs.6,750. What is the compound interest (in Rs.) on the same sum for 2 years at 20% p.a., if interest is compounded half-yearly? (rounded off to the nearest Rs.)

  1. 7,729

  2. 8,702

  3. 8,000

  4. 7858
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

SI = P×R×T/100, so 6750 = P×12×3/100, giving P = 18750. For CI: P = 18750, R = 20% p.a. = 10% half-yearly, T = 2 years = 4 half-years. CI = 18750[(1 + 10/100)^4 - 1] = 18750[1.4641 - 1] = 18750 × 0.4641 = 8701.875 ≈ 8702.

Multiple choice

A certain sum is lent at 4% p.a. for 3 years, 8% p.a. for the next 4 years, and 12% p.a. beyond 7 years. If for a period of 11 years, the simple interest obtained is Rs. 27,600, then the sum is (in Rs):

  1. 20000

  2. 30000

  3. 18000

  4. 25000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the sum be P. Interest for first 3 years at 4% = 0.12P. Interest for next 4 years at 8% = 0.32P. Interest for remaining 4 years at 12% = 0.48P. Total interest = 0.12P + 0.32P + 0.48P = 0.92P = Rs 27,600. Therefore P = 27600/0.92 = Rs 30,000. Option B is correct.

Multiple choice

Surekha borrowed a sum of money and returned it in two equal annual installments of Rs. 5,547 each. If the rate of interest was 7(1/2)% p.c.p.a. compounded yearly, then the total interest paid by her was:

  1. Rs. 1,134

  2. Rs. 1,126

  3. Rs. 1,185

  4. Rs. 1,158
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the present value formula for equal installments: P = 5547/(1 + 7.5/100) + 5547/(1 + 7.5/100)². This gives P = 5160 + 4800 = Rs 9,960. Total amount paid = 5547 × 2 = Rs 11,094. Interest = 11094 - 9960 = Rs 1,134. Option A is correct.

Multiple choice

The rate of interest for first two years is 4%, for next 3 years is 5% and 8% for the period beyond 5 years. If the interest after 7 years is Rs. 1560. Find the principal?

  1. 3000

  2. 5000

  3. 2000

  4. 4000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

माना मूलधन = P। पहले 2 वर्षों का ब्याज = P × 4% × 2 = 0.08P। अगले 3 वर्षों का ब्याज = P × 5% × 3 = 0.15P। शेष 2 वर्षों (कुल 7 वर्ष में से) का ब्याज = P × 8% × 2 = 0.16P। कुल ब्याज = 0.08P + 0.15P + 0.16P = 0.39P। दिया है: 0.39P = 1560, इसलिए P = 1560 / 0.39 = 4000। विकल्प D सही है।

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.40000 at the same rate for 2 years?

  1. 6400

  2. 7500

  3. 7200

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

From the compound interest data, we can find the rate by dividing the amount after 3 years by the amount after 2 years: 314928/291600 = 1.08, giving an 8% annual rate. Simple Interest on Rs.40000 for 2 years at 8% is calculated as SI = (40000 × 8 × 2)/100 = Rs.6400.

Multiple choice

A sum at a certain rate of simple interest becomes Rs. 14880 after 3 years and Rs. 16800 after 5 years. Find the simple interest on the same sum at 10% per annum for 4 years (in Rs.).

  1. 4800

  2. 4500

  3. 4740

  4. 4860
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The interest for 2 years (5-3) is Rs. 16800 - 14880 = Rs. 1920, so annual interest is Rs. 960. Principal = 14880 - (3 × 960) = Rs. 12000. At 10% for 4 years: SI = 12000 × 10 × 4 / 100 = Rs. 4800. Key insight: find annual interest from the difference between the two amounts, then back-calculate principal.

Multiple choice

A man borrowed a certain sum and agrees to repay it by paying Rs. 4000 at the end of first year and Rs. 7700 at the end of second year. If the rate of compound interest compounded annually is 10% per annum, then find the sum (in Rs.) borrowed.

  1. 9000

  2. 115000

  3. 11000

  4. 10000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be borrowed sum. After 1 year at 10%: amount = P × 1.1. Payment of 4000 leaves P × 1.1 - 4000. After 2nd year at 10%: amount = (P × 1.1 - 4000) × 1.1 = P × 1.21 - 4400. This equals 7700. So P × 1.21 = 12100, P = 10000.

Multiple choice

A sum of Rs. 7500 amounts to Rs. 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in Rs.) on the same sum for the same time and the same rate is:

  1. 1500

  2. 1530

  3. 1400

  4. 1485
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, find the time period using compound interest: 7500(1.1)^t = 9075, so (1.1)^t = 1.21, giving t = 2 years. Then calculate simple interest for the same period: SI = P × R × T = 7500 × 0.1 × 2 = Rs. 1500. The key is recognizing that after 2 years at 10%, the compound amount factor is 1.21 (1.1²).

Multiple choice

What is the simple interest on a sum of Rs. 99,000 at 12.5% per annum for a period of 9 months?

  1. Rs. 8,281.25

  2. Rs. 9,281.25

  3. Rs. 9,282.25

  4. Rs. 7,281.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple Interest = Principal × Rate × Time / 100. P = Rs. 99,000, R = 12.5%, T = 9 months = 9/12 years = 3/4 years. SI = 99000 × 12.5 × (3/4) / 100 = 99000 × 12.5 × 0.75 / 100 = 99000 × 9.375 / 100 = Rs. 9,281.25. Options A, C, and D are incorrect calculations.

Multiple choice

A sum of Rs. (x) amounts to Rs. 9,246 in 4 years and to Rs. 11,298.75 in 7.5 years, at (y)% p.a. simple interest. The values of (x) and (y) are, respectively:

  1. 6500 and 8

  2. 6800 and 8.5

  3. 6900 and 8.5

  4. 7200 and 7.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the simple interest formula A = P(1 + rt/100), we have: 9246 = x(1 + 4y/100) and 11298.75 = x(1 + 7.5y/100). Dividing the second equation by the first and solving gives y = 8.5%. Substituting back: 9246 = x(1 + 34/100) = x(1.34), so x = 9246/1.34 = 6900.

Multiple choice

Rahul invested equal sums of money at compound interest under two schemes A and B. Under scheme A, the interest rate was 10% per annum and under scheme B, the interest rate was 12% p.a. The compound interest after two years on the sum invested in scheme A was Rs. 1,050. How much is the interest earned under scheme B after two years, if the interest is compounded annually in both schemes?

  1. Rs. 1,272

  2. Rs. 1,270

  3. Rs. 1,372

  4. Rs. 1,782
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Compound Interest for 2 years at 10% = P[(1 + 10/100)² - 1] = P[(1.1)² - 1] = P[1.21 - 1] = P(0.21). Given CI = Rs. 1050, so P = 1050 / 0.21 = Rs. 5000. For scheme B at 12% for 2 years: CI = 5000[(1 + 12/100)² - 1] = 5000[(1.12)² - 1] = 5000[1.2544 - 1] = 5000 × 0.2544 = Rs. 1272.

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? यदि एक निश्चित राशि पर साधारण ब्याज 3 वर्ष के लिए 4% वार्षिक ब्याज की दर पर 303.60 रुपये है। समान राशि और समान समय और दर पर चक्रवृद्धि ब्याज क्या होगा?

  1. Rs./रु.310.80

  2. Rs./रु.421.70

  3. Rs./रु.315.90

  4. Rs./रु.350.70

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

Simple interest = P × R × T = 303.60, where R = 4% = 0.04, T = 3. So P = 303.60 / (0.04 × 3) = 2530. Compound interest = 2530 × (1 + 0.04)^3 - 2530 = 2530 × 1.124864 - 2530 = 315.90. The difference between CI and SI arises because CI earns interest on accumulated interest.