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 and compound interest on a certain sum for 2 years is INR 1250 and INR 1475, respectively. The rate of interest per annum (compounded annually) in percentage is:

  1. 12

  2. 24

  3. 36

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

For 2 years, SI = 2 * (Principal * Rate) = 1250, so PR = 625. CI = P(1+R)^2 - P = 1475. Substituting P = 625/R into the CI formula: (625/R) * (2R + R^2) = 1475. 1250 + 625R = 1475. 625R = 225. This implies R = 0.36 or 36%.

Multiple choice

Maria deposits x dollars in a savings account with an annual interest rate of 10%, compounded annually. One year later, she deposits an additional x dollars. If the balance after two years is w dollars, then which expression shows x in terms of w?

  1. w 1 + 1.10

  2. w 1.10 + 1.15

  3. w 1.10 + 1.331

  4. w 1.10 + ( 1.10 ) 2

  5. w ( 1.10 ) 2 + ( 1.10 ) 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The first deposit earns interest for two years and becomes 1.10^2 x, while the second deposit earns interest for one year and becomes 1.10x. Hence w = x[1.10 + (1.10)^2], so x = w/[1.10 + (1.10)^2].

Multiple choice

A sum of money is invested at a rate of 12% per annum. The interest is compounded annually. The difference between the compound interest and simple interest earned over 2 years is Rs. 144. What is the principal (initial sum) invested?

  1. Rs. 8,000

  2. Rs. 9,000

  3. Rs. 10,000

  4. Rs. 12,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Difference between CI and SI for 2 years is P * (r/100)^2. 144 = P * (12/100)^2. 144 = P * (0.12)^2. 144 = P * 0.0144. P = 144 / 0.0144 = 10000.

Multiple choice

Emma deposited x dollars at an annual interest rate of 6%, compounded annually. After one year, she deposited another x dollars into the same account. If the total amount in her account after two years was y dollars, then which of the following expresses x in terms of y?

  1. y 1 + 1.06

  2. y 1.06 + 1.12

  3. y 1.06 + 1.18

  4. y 1.06 + (1.06) 2

  5. y (1.06) 2 + (1.06) 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After one year, the first deposit x grows to x(1.06). Then another x is added, making the total x(1.06) + x. After the second year, this entire amount grows by 6%, resulting in (x(1.06) + x)(1.06) = x(1.06)^2 + x(1.06) = y. Factoring out x gives x(1.06 + 1.06^2) = y, so x = y / (1.06 + 1.06^2).

Multiple choice

A small business owner deposits some money in a fixed-return plan that pays simple interest at a constant annual rate. The deposit grows to Rs. 13,440 after 4 years and to Rs. 16,320 after 7 years. If the same deposit had instead been placed for 2 years in a recurring plan that compounds every 6 months at the same annual rate, then the total interest earned (approximately) would be:

  1. Rs. 1,950

  2. Rs. 2,070

  3. Rs. 2,250

  4. Rs. 2,430
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Liam deposits $10,000 into a fixed deposit account offering 6% annual simple interest. After 3 years, he withdraws half of the principal. How much interest will he have earned by then, and what is the total balance in his account after this withdrawal?
  1. Interest: \$1,200; Total balance after withdrawal: \$6,200
  2. Interest: \$1,500; Total balance after withdrawal: \$6,500
  3. Interest: \$1,800; Total balance after withdrawal: \$7,000
  4. Interest: \$1,800; Total balance after withdrawal: \$6,800
  5. Interest: \$1,900; Total balance after withdrawal: \$7,200
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Sophia invested her inheritance in a real estate fund, which grew to \$15,000 by the end of the 2nd year and increased to \$18,000 by the end of the 3rd year under compound interest. What is the annual compound interest rate?

  1. 18.5%

  2. 19.5%

  3. 20%

  4. 21%

  5. 22.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The amount grows from 15,000 to 18,000 in one year (from end of year 2 to end of year 3). The interest earned is 3,000. The rate is (3,000 / 15,000) * 100 = 20%.

Multiple choice

A principal amount is placed in a simple-interest deposit. It becomes Rs. 17,500 after 5 years and Rs. 21,500 after 9 years. If the same principal amount were instead invested for 3 years at the same nominal annual rate, compounded half yearly, approximately how much interest (in rupees) would it earn?

  1. Rs. 3,713

  2. Rs. 3,731

  3. Rs. 3,317

  4. Rs. 3,371
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest: P + 5I = 17500, P + 9I = 21500. 4I = 4000, I = 1000. P = 17500 - 5000 = 12500. Rate R = (1000/12500) * 100 = 8%. Compound interest for 3 years half-yearly at 8% p.a. (4% per half-year, 6 periods): 12500 * (1.04^6 - 1) = 12500 * (1.2653 - 1) = 12500 * 0.2653 = 3316.25.

Multiple choice

Priya divided her total investment into two parts. The simple interest earned on the first part at 18% per annum for 5 years is equal to the simple interest earned on the second part at 15% per annum for 4 years. What percentage of the total amount did Priya invest in the first part?

  1. 30%

  2. 35%

  3. 40%

  4. 45%

  5. 60%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let parts be P1 and P2. (P1 * 18 * 5) / 100 = (P2 * 15 * 4) / 100. 90*P1 = 60*P2. P1/P2 = 60/90 = 2/3. P1 is 2/(2+3) = 2/5 = 40% of total.

Multiple choice

An individual invests $5,000 in three different investment schemes for one year. Scheme A offers a fixed interest rate of 9% per annum, Scheme B offers a compound interest rate of 8% per annum calculated semi-annually, and Scheme C offers a compound interest rate of 8% per annum calculated quarterly. Which scheme would yield the highest return on the investment after one year?

  1. Scheme A

  2. Scheme B

  3. Scheme C

  4. All the above Scheme provide same return.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Scheme A: 9% simple interest = 5000 * 0.09 = 450. Scheme B: 8% compounded semi-annually = 5000 * (1 + 0.04)^2 - 5000 = 5000 * 1.0816 - 5000 = 408. Scheme C: 8% compounded quarterly = 5000 * (1 + 0.02)^4 - 5000 = 5000 * 1.0824 - 5000 = 412. Scheme A yields the highest return.

Multiple choice

Sunita borrows Rs. 4 lakhs at an interest rate of 10% per annum, compounded half-yearly. She repays Rs. 24,200 at the end of the first year and settles the remaining loan at the end of the third year. The total interest, in rupees, paid over the three years is nearest to:

  1. 1,03,200

  2. 1,03,280

  3. 1,30,823

  4. 1,13,820
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = 400,000. Rate = 10% p.a. compounded half-yearly (5% every 6 months). Year 1: 400,000 * (1.05)^2 = 441,000. Repay 24,200, balance = 416,800. Year 2: 416,800 * (1.05)^2 = 459,558. Year 3: 459,558 * (1.05)^2 = 506,658. Total interest = 506,658 + 24,200 - 400,000 = 130,858. Nearest option is 1,30,823.

Multiple choice

Rekha started with a total sum of Rs. 36,000. She allocated Rs. 14,000 to a fixed deposit at 6.2% per annum, Rs. 10,000 to another account earning 5.12% per annum, and placed the rest of the amount in a third account offering r% simple interest annually. Her overall yearly income from all three deposits was equal to 5.5% of her initial capital. If Rekha had chosen to invest the entire Rs. 36,000 at the rate of (r + 3)%, then what would have been her annual return (in Rs.)?

  1. 2,280

  2. 2,440

  3. 2,880

  4. 2,840
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total income = 36000 * 0.055 = 1980. Income from 14000 at 6.2% = 868. Income from 10000 at 5.12% = 512. Remaining 12000 at r% = 1980 - 868 - 512 = 600. So r = (600/12000)*100 = 5%. New rate = 5+3 = 8%. Return = 36000 * 0.08 = 2880.

Multiple choice

An investor deposits Rs. 1,500 in an account earning interest compounded annually at r%. He withdraws Rs. 720 at the end of the first year and Rs. 972 at the end of the second year. After the second withdrawal, the balance becomes zero. Find r.

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Year 1: 1500(1+r/100) - 720 = Balance. Year 2: Balance(1+r/100) - 972 = 0. Let x = 1+r/100. 1500x - 720 = B. (1500x - 720)x = 972. 1500x^2 - 720x - 972 = 0. Divide by 12: 125x^2 - 60x - 81 = 0. Using quadratic formula: x = [60 +/- sqrt(3600 - 4*125*-81)] / 250 = [60 +/- sqrt(3600 + 40500)] / 250 = [60 +/- sqrt(44100)] / 250 = [60 + 210] / 250 = 270/250 = 1.08. r = 8%.

Multiple choice

A company invested a total of Rs. 36 lakh in three different portfolios. A part of the amount was allocated to a high-yield bond offering 9% annual interest. The remaining amount was divided between two mutual funds in the ratio 3 : 2, earning 6% and 5% annual interest, respectively. If the total annual return from all investments was Rs. 2.56 lakh, what was the amount (in Rs. lakh) invested in the high-yield bond?

  1. 8

  2. 12

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount in the 9% bond. Remaining amount = 36 - x. Mutual funds get 3/5 * (36 - x) at 6% and 2/5 * (36 - x) at 5%. Total interest = 0.09x + 0.06 * 0.6 * (36 - x) + 0.05 * 0.4 * (36 - x) = 2.56. 0.09x + 0.036(36-x) + 0.02(36-x) = 2.56. 0.09x + 0.056(36-x) = 2.56. 0.034x = 2.56 - 2.016 = 0.544. x = 16.