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

John took a loan for his home renovation at a simple interest rate of 5% per annum for the first year. The interest rate increased by 2% per annum for each subsequent year. After 4 years, he paid a total of $8,000 as interest. What was the loan amount?
  1. $20,000
  2. $22,500
  3. $25,000
  4. $27,500
  5. $30,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal. Interest = P * (5/100 * 1 + 7/100 * 1 + 9/100 * 1 + 11/100 * 1) = P * (32/100) = 8000. P = 8000 * 100 / 32 = 25000.

Multiple choice

John and Mary each invested \$2,500 in different financial institutions for 3 years. Both investments were made in simple interest-bearing accounts. At the end of 3 years, John received \$75 more in interest from his investment than Mary. If the rate of interest on Mary's investment was 5% per annum, what was the rate of interest on John's investment?

  1. 6%

  2. 7%

  3. 8%

  4. 9%

  5. 10%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let R be John's rate. Interest = (P * R * T) / 100. John's interest - Mary's interest = 75. (2500 * R * 3)/100 - (2500 * 5 * 3)/100 = 75. 75R - 375 = 75. 75R = 450. R = 6%.

Multiple choice

Tom, a homeowner in Chicago, decided to take a loan of \$40,000 to renovate his house. He borrowed part of the money at an interest rate of 10% per annum, and the rest at an interest rate of 15% per annum. After 1 year, Tom repaid a total of \$5,700 in interest. How much did he borrow at each interest rate?
  1. $6,000 at 10%, $34,000 at 15%
  2. $10,000 at 10%, $30,000 at 15%
  3. $12,000 at 10%, $28,000 at 15%
  4. $15,000 at 10%, $25,000 at 15%
  5. $20,000 at 10%, $20,000 at 15%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount at 10% and y be the amount at 15%. x + y = 40000 and 0.10x + 0.15y = 5700. Multiplying the first by 0.10 gives 0.10x + 0.10y = 4000. Subtracting this from the second gives 0.05y = 1700, so y = 34000. Then x = 6000.

Multiple choice

A financial advisor, Mr. Brian noticed that his annual income from interest on investments had decreased due to a change in the market interest rates. Previously, his investments earned him an annual return at a rate of 10%, but due to recent economic shifts, the interest rate dropped to 6%. This change resulted in a decrease of $120 in his annual income. What was the original amount of capital Mr. Brian had invested?
  1. $3,000
  2. $4,000
  3. $5,000
  4. $6,000
  5. $6,500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P be the principal. The decrease in interest is 10% of P - 6% of P = 4% of P. Given 0.04 * P = 120, P = 120 / 0.04 = 3000.

Multiple choice

Sarah, an investment banker, decided to lend a sum of money to a friend who wanted to open a small café. They agreed on an annual simple interest rate of 5%. Sarah lent her friend $15,000. If the interest accrued for a specific period was to be calculated from March 1, 2023, to June 15, 2023, approximately how much simple interest would Sarah earn for that period?
  1. $150
  2. $180
  3. $220
  4. $250
  5. $300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Time period: March (31-1) + April (30) + May (31) + June (15) = 30 + 30 + 31 + 15 = 106 days. Simple Interest = (P * R * T) / 100 = (15000 * 0.05 * 106) / 365 = 750 * 106 / 365 = 79500 / 365 = 217.80. This rounds to approximately $220.

Multiple choice

The difference, after two years, between the compound interest and the simple interest on a certain sum of money invested at the same rate of interest is \$25. If the simple interest accumulated on the sum after two years is \$200, what is the rate of interest at which the sum of money was invested?

  1. 18%

  2. 20%

  3. 25%

  4. 28%

  5. 30%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

SI for 2 years = 200, so SI for 1 year = 100. CI - SI for 2 years = 25. Formula: CI - SI = P(r/100)^2. Also SI = P*r*t/100 = 200. P*r = 10000. (P*r^2)/10000 = 25 -> (10000*r)/10000 = 25 -> r = 25%.

Multiple choice

Emily has invested money in two different accounts to fund for her retirement. One account gives her an annual simple interest rate of 4%, while the other provides a rate of 6%. After 3 years, her total income from both investments is $1,200. Additionally, one-half of the amount invested in the first account is equal to one-fourth of the amount invested in the second account. If Emily's total investment is the sum of money invested in these two accounts, how much has she invested in total?
  1. $5,000
  2. $5,800
  3. $6,500
  4. $7,500
  5. $8,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x and y be the amounts in the two accounts. We have 0.04x*3 + 0.06y*3 = 1200, which simplifies to 0.12x + 0.18y = 1200, or 2x + 3y = 20000. Also, 0.5x = 0.25y, so y = 2x. Substituting y = 2x into the first equation: 2x + 3(2x) = 20000, so 8x = 20000, x = 2500. Then y = 5000. Total investment = 2500 + 5000 = 7500.

Multiple choice

Ramesh invests ₹1,200 at 5% simple interest. How much additional money must he invest at 8% simple interest so that his total annual income will be equal to 6% of his total investment during this year?

  1. ₹500

  2. ₹600

  3. ₹1,200

  4. ₹1,500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the additional amount. Total investment = 1200 + x. Total interest = 0.05 * 1200 + 0.08 * x. We want total interest = 0.06 * (1200 + x). 60 + 0.08x = 72 + 0.06x. 0.02x = 12, so x = 600.

Multiple choice

On a certain sum of money the compound interest Rs. 318 is earned in 2 years. If the rate of interest is 12%, what is the principal amount?

  1. Rs. 1250

  2. Rs.1300

  3. Rs. 1200

  4. Rs. 1150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for compound interest over 2 years is CI = P * ((1 + r/100)^2 - 1). Substituting the given values, we get 318 = P * ((1.12)^2 - 1), which simplifies to 318 = P * 0.2544. Solving for P gives a principal amount of Rs. 1250.

Multiple choice

A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs. 180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs. 120. For how many years was the sum invested?

  1. 24 years

  2. 22 years

  3. 25 years

  4. 23 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and T be the time. SI = P * R * T / 100. Amount = P + SI. So, P(1 + 0.08T) = 180 and P(1 + 0.04T) = 120. Dividing the two equations: (1 + 0.08T) / (1 + 0.04T) = 180/120 = 1.5. Solving for T: 1 + 0.08T = 1.5 + 0.06T, which gives 0.02T = 0.5, so T = 25.

Multiple choice

The simple interest on a certain sum of money at rate of interest 5% per annum for 2 years is Rs. 500. What is the compound interest on the same sum for the same period and at the same rate of interest?

  1. Rs.412.5

  2. Rs.400

  3. Rs.500

  4. Rs.512.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple interest (SI) = P * r * t / 100. 500 = P * 0.05 * 2, so P = 5000. Compound interest (CI) = P * ((1 + r/100)^t - 1) = 5000 * ((1.05)^2 - 1) = 5000 * (1.1025 - 1) = 5000 * 0.1025 = 512.5.

Multiple choice

Rahul borrows Rs. 3,00,000 at an annual interest rate of 10%, compounded yearly. He repays Rs. 20,000 at the end of the first year and settles the remaining balance at the end of the fourth year. The total interest paid over the four years, in rupees, is approximately:

  1. Rs. 1,02,610

  2. Rs. 1,20,000

  3. Rs. 1,25,410

  4. Rs. 1,32,610

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

Year 1: 300000 * 1.1 = 330000. Pay 20000, balance = 310000. Year 2: 310000 * 1.1 = 341000. Year 3: 341000 * 1.1 = 375100. Year 4: 375100 * 1.1 = 412610. Total paid = 20000 + 412610 = 432610. Total interest = 432610 - 300000 = 132610.

Multiple choice

Ravi invests Rs. 18,000 for 6 years in a scheme with 6% interest per annum, compounded annually. Separately, Manoj invests a certain amount in the same scheme for 4 years, and then reinvests the entire amount he receives at the end of 4 years, for two years at 3% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Manoj is

  1. 17,400

  2. 18,250

  3. 18,070

  4. 19,080

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

Ravi: 18000 * (1.06)^6. Manoj: Let M be investment. After 4 years, amount = M * (1.06)^4. Then reinvested for 2 years at 3% SI: Amount = M * (1.06)^4 * (1 + 0.03 * 2) = M * (1.06)^4 * 1.06 = M * (1.06)^5. Equating: 18000 * (1.06)^6 = M * (1.06)^5. M = 18000 * 1.06 = 19080.