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

Sara invested a certain amount of money in two different schemes. In Scheme A, she earned \$1600 as simple interest after 2 years at 8% rate of interest. In Scheme B, she earned \$3570 as compound interest after 2 years. The rate of interest for Scheme B is 10% per annum. What is the ratio of the amount Sara invested in Scheme A to the amount she invested in Scheme B?

  1. 15 : 18

  2. 23 : 37

  3. 17 : 9

  4. 10 : 17
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For Scheme A: SI = 1600, R = 8%, T = 2 years. P = (1600*100)/(8*2) = 10000. For Scheme B: CI = 3570, R = 10%, T = 2 years. Amount = P(1 + 10/100)^2 = 1.21P. CI = 0.21P = 3570, so P = 3570/0.21 = 17000. Ratio = 10000 : 17000 = 10 : 17.

Multiple choice

Sarita invests a sum of money at a rate of 5% p.a. simple interest and another sum at a rate of 7% p.a. simple interest. Her total interest income after 2 years is Rs. 726. Also, one-third of the first sum is equal to one-fifth of the second sum. Find the total amount invested.

  1. Rs. 5,808

  2. Rs. 5,800

  3. Rs. 5,670

  4. Rs. 5,404

  5. Rs. 5,900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sums be S1 and S2. S1/3 = S2/5 => S2 = 5/3 * S1. Interest: (S1 * 0.05 * 2) + (S2 * 0.07 * 2) = 726. 0.1 * S1 + 0.14 * (5/3 * S1) = 726. 0.1 * S1 + 0.2333 * S1 = 726. 0.3333 * S1 = 726 => S1 = 2178. S2 = 3630. Total = 5808.

Multiple choice

Rajat lends Rs. 10,000 for 3 years at an interest rate of 15% per annum. Manoj lends the same amount for 3 years in the ratio 5 : 7 : 8 with interest rates of 8%, 15%, and x%, respectively. If Rajat earns 10% less interest than Manoj, what is the value of x?

  1. 24.125%

  2. 25.176%

  3. 23.541%

  4. 24.115%

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

Rajat's interest = 10000 * 3 * 0.15 = 4500. Manoj's principal is split in 5:7:8 ratio (total 20 parts). Principal 1 = 2500, P2 = 3500, P3 = 4000. Interest = 2500*3*0.08 + 3500*3*0.15 + 4000*3*(x/100) = 600 + 1575 + 120x = 2175 + 120x. Rajat earns 10% less than Manoj, so 4500 = 0.9 * (2175 + 120x). 5000 = 2175 + 120x, 2825 = 120x, x = 23.5416%.

Multiple choice

Mayur lends a certain sum for 2 years at 20% rate of interest and gets Rs. 500 as interest. If Mayur's investment is the same as the interest Ram gets by investing a certain sum after 5 years at 10% interest, find the sum invested by Ram.

  1. Rs. 3,750

  2. Rs. 2,500

  3. Rs. 3,600

  4. Rs. 4,000

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

Mayur's interest is 500 for 2 years at 20% (SI), so his principal is 500 / (0.2 * 2) = 1250. Ram's interest is 1250 over 5 years at 10% (SI), so 1250 = P * 0.1 * 5, which means P = 1250 / 0.5 = 2500.

Multiple choice

A man borrows Rs. 15,150, which is to be paid back with compound interest at a rate of 2% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

  1. Rs. 7,803

  2. Rs. 7,808

  3. Rs. 2,601

  4. Rs. 5,050

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

For two equal annual installments P at rate r=2%, the formula is Total = P/(1+r) + P/(1+r)^2. 15150 = P/1.02 + P/(1.02)^2. 15150 = P * (1/1.02 + 1/1.0404) = P * (1.02 + 1)/1.0404 = P * 2.02/1.0404. P = 15150 * 1.0404 / 2.02 = 7803.

Multiple choice

A sum invested at a certain rate of interest becomes double in 10 years at simple interest. What will be the percent return, if the sum is invested at the same rate of interest compounded annually for three years?

  1. 27.4%

  2. 29.2%

  3. 33.1%

  4. 35.1%

  5. 37.4%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest: P becomes 2P in 10 years, so interest = P. P = P * r * 10 / 100, so r = 10%. Compound interest for 3 years: Amount = P(1 + 10/100)^3 = P(1.1)^3 = 1.331P. Return = 33.1%.

Multiple choice

Bank X offers investment in three different schemes A, B and C. Schemes A, B and C respectively offer 15%, 20% and 25% rates of interest compounded annually. Ram invests 50% of his money in scheme A, 50% of remaining in scheme B and remaining in scheme C. What will be his percent return at the end of three years?

  1. 56%

  2. 64%

  3. 68%

  4. 72%

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

Let total money = 100. Scheme A: 50 invested at 15% for 3 years = 50 * (1.15)^3 = 50 * 1.520875 = 76.04. Scheme B: 25 invested at 20% for 3 years = 25 * (1.2)^3 = 25 * 1.728 = 43.2. Scheme C: 25 invested at 25% for 3 years = 25 * (1.25)^3 = 25 * 1.953125 = 48.83. Total = 76.04 + 43.2 + 48.83 = 168.07. Return = 68%.

Multiple choice

Raj deposited a specific sum in a bank at an annual compound interest rate. If the interest earned at the end of the third and fifth years amounts to Rs. 700 and Rs. 1,450.50, respectively, calculate the interest accrued by him if the amount is deposited for the eleven years, expressed in INR.

  1. 2,905.56

  2. 6,925.65

  3. 12,905.56

  4. 19,205.65

  5. 30,105.65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and r be the annual interest rate. Interest at end of year n is P(1+r)^(n-1)*r. Ratio of interest at year 5 to year 3 is (1+r)^2 = 1450.50 / 700 = 2.07214. Thus 1+r = sqrt(2.07214) = 1.44. The interest at year 11 is 700 * (1.44)^8 = 700 * 18.4365 = 12905.56.

Multiple choice

A refrigerator costs Rs. 1,08,000. After making a down payment of Rs. 20,000, the remaining amount is financed at an annual interest rate of 9% to be repaid over 4 equal quarterly instalments. What is the quarterly instalment amount (to the nearest hundreds integer)?

  1. Rs. 20,200

  2. Rs. 22,800

  3. Rs. 23,200

  4. Rs. 23,800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = 108,000 - 20,000 = 88,000. Quarterly rate = 9%/4 = 2.25% = 0.0225. Using EMI formula P = A * [1 - (1+r)^-n] / r. 88,000 = A * [1 - (1.0225)^-4] / 0.0225. 88,000 = A * [1 - 0.9145] / 0.0225. 88,000 = A * 3.802. A = 88,000 / 3.802 = 23,145. Nearest hundred is 23,100 or 23,200.

Multiple choice

Sumit has Rs. 90,000 with him. He purchases three items A, B, and C for Rs. 15,000, Rs. 13,000, and Rs. 35,000 respectively and puts the remaining money in a bank deposit that pays compound interest @15% per annum. After 2 years, he sells off the three items at 80% of their original price and also withdraws his entire money from the bank by closing the account. What is the total change in his asset?

  1. -4.152%

  2. +3.152%

  3. -4.325%

  4. +5.552%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial assets: 90,000. Spent: 15k+13k+35k = 63k. Remaining in bank: 27k. After 2 years, bank money = 27000 * (1.15)^2 = 27000 * 1.3225 = 35707.5. Items sold at 80%: 63000 * 0.8 = 50400. Total final assets = 35707.5 + 50400 = 86107.5. Change = 86107.5 - 90000 = -3892.5. Percentage change = -3892.5 / 90000 = -4.325%.