Compound Interest


  1. A money-lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains ₹ 104.50 a year. The amount of money he borrows, is









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    Let the borrowed amount be y
    According to the question,

    y 1 +
    3
    2 − 1
    y × 4 × 1
    = 104.50
    100100

    [∵  Interest is compounded half yearly]
    ⇒  y [(1.03)2 – 1] – 0.04y = 104.50

    Correct Option: C

    Let the borrowed amount be y
    According to the question,

    y 1 +
    3
    2 − 1
    y × 4 × 1
    = 104.50
    100100

    [∵  Interest is compounded half yearly]
    ⇒  y [(1.03)2 – 1] – 0.04y = 104.50
    ⇒  0.0609y – 0.04y = 104.50
    ⇒  0.0209y = 104.5
    ⇒  y =
    104.5
    = ₹ 5000
    0.0209


  1. A person deposited a sum of ₹ 6,000 in a bank at 5% per annum simple interest. Another
    person deposited ₹ 5,000 at 8% per annum compound interest. After two years, the difference of their interests will be









  1. View Hint View Answer Discuss in Forum

    Here , sum = ₹ 6,000 , Rate = 5% per annum , T = 2 years

    S.I.=
    6000 × 5 × 2
    = ₹ 600
    100

    C.I. = 5000 1 +
    8
    2 − 1
    100

    C.I. = 5000
    27
    2 − 1
    25

    Correct Option: B

    Here , sum = ₹ 6,000 , Rate = 5% per annum , T = 2 years

    S.I.=
    6000 × 5 × 2
    = ₹ 600
    100

    C.I. = 5000 1 +
    8
    2 − 1
    100

    C.I. = 5000
    27
    2 − 1
    25

    C.I. = 5000
    729 − 625
    625

    C.I. = 5000 ×
    104
    = ₹ 832
    625

    ∴  Required difference = C.I. - S.I.
    ∴  Required difference = ₹ (832–600) = ₹ 232



  1. The income of a company increases 20% per year. If the income is Rs. 26,64,000 in the year
    2012, then its income in the year 2010 was :









  1. View Hint View Answer Discuss in Forum

    Given in question , Income = Rs. 26,64,000 , Rate = 20%
    Let the income of company in 2010 be Rs. P
    According to the question,

    A = P1 +
    R
    T
    100

    ⇒  2664000 = P1 +
    20
    2
    100

    ⇒  2664000 = P1 +
    1
    2
    5

    Correct Option: B

    Given in question , Income = Rs. 26,64,000 , Rate = 20%
    Let the income of company in 2010 be Rs. P
    According to the question,

    A = P1 +
    R
    T
    100

    ⇒  2664000 = P1 +
    20
    2
    100

    ⇒  2664000 = P1 +
    1
    2
    5

    ⇒  2664000 = P ×
    6
    2
    5

    ⇒  P =
    2664000 × 5 × 5
    = Rs. 1850000
    6 × 6


  1. Mr. Dutta desired to deposit his retirement benefit of Rs. 3 lacs partly to a post office and partly to a bank at 10% and 6% interests respectively. If his monthly interest income was Rs. 2000, then the difference of his deposits in the post office and in the bank was :









  1. View Hint View Answer Discuss in Forum

    Let the amount deposited in Post Office be Rs. y lakhs.
    ∴ Amount deposited in bank = Rs. (3 – y) lakhs
    According to the question,

    y × 10 × 1
    +
    (3 – y) × 6 × 1
    100 × 12100 × 12

    =
    2000
    =
    1
    10000050

    ⇒ 10y + 18 – 6y =
    1
    × 1200 = 24
    50

    ⇒  4y = 24 – 18 = 6

    Correct Option: C

    Let the amount deposited in Post Office be Rs. y lakhs.
    ∴ Amount deposited in bank = Rs. (3 – y) lakhs
    According to the question,

    y × 10 × 1
    +
    (3 – y) × 6 × 1
    100 × 12100 × 12

    =
    2000
    =
    1
    10000050

    ⇒ 10y + 18 – 6y =
    1
    × 1200 = 24
    50

    ⇒  4y = 24 – 18 = 6
    ⇒  y =
    6
    = Rs.
    3
    lakhs
    42

    ∴  Required difference = 0



  1. A sum of money is paid back in two annual instalments of Rs. 17, 640 each, allowing 5% compound interest compounded annually. The sum borrowed was









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    According to question ,
    Sum borrowed = Present worth of Rs. 17640 due 1 year hence + Present worth of Rs. 17640 due 2 years hence

    = Rs.17640 ×
    20
    + 17640 ×
    20
    ×
    20
    212121

    Correct Option: A

    According to question ,
    Sum borrowed = Present worth of Rs. 17640 due 1 year hence + Present worth of Rs. 17640 due 2 years hence

    = Rs.17640 ×
    20
    + 17640 ×
    20
    ×
    20
    212121

    sum borrowed = Rs. (16800 + 16000) = Rs. 32800