Compound Interest


  1. The compound interest on ₹ 8,000 at 15% per annum for 2 years 4 months, compounded annually is:









  1. View Hint View Answer Discuss in Forum

    Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
    Using the given formula ,

    Amount = P1 +
    R
    t
    100

    Amount = 80001 +
    15
    7/3
    100

    Amount = 80001 +
    3
    21 +
    3
    2020 × 3

    Correct Option: C

    Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
    Using the given formula ,

    Amount = P1 +
    R
    t
    100

    Amount = 80001 +
    15
    7/3
    100

    Amount = 80001 +
    3
    21 +
    3
    2020 × 3

    Amount = 8000 ×
    23
    ×
    23
    ×
    21
    = ₹ 11109
    202020

    ∴  Compound Interest = Amount - Principal
    ∴  Compound Interest = ₹ (11109 – 8000) = ₹ 3109


  1. At what rate per annum will ₹ 32000 yield a compound interest of ₹ 5044 in 9 months interest being compounded quarterly ?









  1. View Hint View Answer Discuss in Forum

    Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
    Let the rate of CI be R percent per annum.

    ∴  CI = P 1 +
    R
    T − 1
    100

    ⇒  5044 = 32000 1 +
    R
    3 − 1
    400

    [∵  Interest is compounded quarterly]
    ⇒ 
    5044
    = 1 +
    R
    3 − 1
    32000400

    ⇒  1 +
    R
    3 − 1 =
    1261
    4008000

    ⇒  1 +
    R
    3 = 1 +
    1261
    4008000

    ⇒  1 +
    R
    3 =
    9261
    =
    21
    3
    400800020

    Correct Option: A

    Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
    Let the rate of CI be R percent per annum.

    ∴  CI = P 1 +
    R
    T − 1
    100

    ⇒  5044 = 32000 1 +
    R
    3 − 1
    400

    [∵  Interest is compounded quarterly]
    ⇒ 
    5044
    = 1 +
    R
    3 − 1
    32000400

    ⇒  1 +
    R
    3 − 1 =
    1261
    4008000

    ⇒  1 +
    R
    3 = 1 +
    1261
    4008000

    ⇒  1 +
    R
    3 =
    9261
    =
    21
    3
    400800020

    ⇒  1 +
    R
    =
    21
    R
    =
    21
    − 1 =
    1
    400204002020

    ⇒  R =
    400
    = 20
    20



  1. The compound interest on ₹ 2000 in 2 years if the rate of interest is 4% per annum for the first year and 3% per annum for the second year, will be









  1. View Hint View Answer Discuss in Forum

    Given Here , R1 = 4% , R2 = 3% , P = ₹ 2000
    Using formula ,

    Amount = P1 +
    R1
    1 +
    R2
    100100

    Amount = 20001 +
    4
    1 +
    3
    100100

    Correct Option: A

    Given Here , R1 = 4% , R2 = 3% , P = ₹ 2000
    Using formula ,

    Amount = P1 +
    R1
    1 +
    R2
    100100

    Amount = 20001 +
    4
    1 +
    3
    100100

    Amount = 2000 × 1.04 × 1.03 = ₹ 2142.40
    ∴  CI = Amount - Principal
    ∴  CI = ₹ (2142.40 – 2000) = ₹ 142.40


  1. If the rate of interest be 4% per annum for first year, 5% per annum for second year and 6% per annum for third year, then the compound interest of ₹ 10,000 for 3 years will be









  1. View Hint View Answer Discuss in Forum

    Given that , R1 = 4% , R2 = 5% , R3 = 6% , P = ₹ 10,000
    Using the given formula ,

    Amount = P1 +
    R1
    1 +
    R2
    1 +
    R3
    100100100

    Amount = 100001 +
    4
    1 +
    5
    1 +
    6
    100100100

    Correct Option: C

    Given that , R1 = 4% , R2 = 5% , R3 = 6% , P = ₹ 10,000
    Using the given formula ,

    Amount = P1 +
    R1
    1 +
    R2
    1 +
    R3
    100100100

    Amount = 100001 +
    4
    1 +
    5
    1 +
    6
    100100100

    Amount = 10000 ×
    26
    ×
    21
    ×
    53
    = ₹ 11575.2
    252050

    ∴  C.I. = Amount - Principal
    ∴  C.I. = ₹ (11575.2 – 10000) = ₹ 1575.2



  1. The compound interest on ₹ 16,000 for 9 months at 20% per annum, interest being compounded quarterly, is









  1. View Hint View Answer Discuss in Forum

    The interest is compounded quarterly.

    ∴  R =
    20
    = 5%
    4

    Time = 3 quarters , P = ₹ 16,000
    ∴  C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 16000 1 +
    5
    3 − 1
    100

    C.I. = 16000
    21
    3 − 1
    20

    Correct Option: C

    The interest is compounded quarterly.

    ∴  R =
    20
    = 5%
    4

    Time = 3 quarters , P = ₹ 16,000
    ∴  C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 16000 1 +
    5
    3 − 1
    100

    C.I. = 16000
    21
    3 − 1
    20

    C.I. = 16000
    9261 − 8000
    8000

    C.I. = 16000 ×
    1261
    = ₹ 2522
    8000