Compound Interest

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  1. Income of Shantanu was ₹ 4000. In the first 2 yr. his income decreased by 10% and 5% respectively but in the third year, the income increased by 15%. What was his income at the end of third year ?








  1. View Hint View Answer Discuss in Forum

    Given, P = ₹ 4000
    R1= 10% (decreased), R2 = 5% (decreases) and R3 = 15% (growth)
    ∴ According to the formula,
    Income at the end of third year = P(1 - R1/100)(1 - R2/100)(1 + R3/100)
    = 4000(1- 10/100) (1 - 5/100) (1 + 15/100)

    Correct Option: A

    Given, P = ₹ 4000
    R1= 10% (decreased), R2 = 5% (decreases) and R3 = 15% (growth)
    ∴ According to the formula,
    Income at the end of third year = P(1 - R1/100)(1 - R2/100)(1 + R3/100)
    = 4000(1- 10/100) (1 - 5/100) (1 + 15/100)
    = 4000 x (9/10) x (19/20) x (23/20)
    = 9 x 19 x 23
    = ₹ 3933

  1. A man borrows ₹ 5100 to be paid back with compound interest at the rate of 4 % pa by the end of 2 yr in two equal yearly installments. How much will each installment be ?








  1. View Hint View Answer Discuss in Forum

    Let each installment be ₹ N .
    Then , according to the question ,
    N/(1 + 4/100 ) + N/(1 + 4/100 )2 = 5100
    ⇒ 25N/26 + 625N/676 = 5100
    ⇒ 1275N = 5100 x 676

    Correct Option: A

    Let each installment be ₹ N .
    Then , according to the question ,
    N/(1 + 4/100 ) + N/(1 + 4/100 )2 = 5100
    ⇒ 25N/26 + 625N/676 = 5100
    ⇒ 1275N = 5100 x 676
    ∴ N = (5100 x 676)/1275 = ₹ 2704

  1. A sum invested for 3 yr compounded at 5%, 10% and 20% respectively. In 3 yr, if the sum amounts to ₹ 16632, then find the sum.








  1. View Hint View Answer Discuss in Forum

    Let the required sum be P Then,
    P (1 + 5/100) (1 + 10/100) (1 + 20/100) = 16632

    Correct Option: B

    Let the required sum be P Then,
    P (1 + 5/100) (1 + 10/100) (1 + 20/100) = 16632
    ⇒ P x (105/100) x (110/100) x (120/100) = 16632
    ⇒ P = 16632 x [(100 x 100 x 100) / (105 x 110 x 120)]
    ∴ P = ₹ 12000

  1. The simple interest for certain sum in 2 yr at 4% pa is ₹ 80. What will be the compound interest for the same sum, if conditions of rate and time period are same ?








  1. View Hint View Answer Discuss in Forum

    Given, n = 2 yr, R = 4% and SI = 80
    According to the formula,
    CI = SI(1 + 4/200)

    Correct Option: B

    Given, n = 2 yr, R = 4% and SI = 80
    According to the formula,
    CI = SI(1 + 4/200) = 80 x 51/50 = ₹ 81.60

  1. A sum of money lent at compound interest for 2 yr at 20 % pa would fetch ₹ 964 more, if the interest was payable half-yearly than if it was payable annually. What is the sum ?








  1. View Hint View Answer Discuss in Forum

    Let the sum be ₹ P .
    Then, CI when compounded half - yearly = [P x (1 + 10/100)4 - P] = 4641P/10000
    CI when compounded annually = [ P x (1 + 20/100)2 - P] = 11P/25
    According to the question, 4641P/10000 - 11P/25 = 964
    ⇒ [(4641 - 4400)/10000] x P = 964

    Correct Option: A

    Let the sum be ₹ P .
    Then, CI when compounded half - yearly = [P x (1 + 10/100)4 - P] = 4641P/10000
    CI when compounded annually = [ P x (1 + 20/100)2 - P] = 11P/25
    According to the question, 4641P/10000 - 11P/25 = 964
    ⇒ [(4641 - 4400)/10000] x P = 964
    ∴ P = (964 x 10000)/241
    = ₹ 40000