Compound Interest


  1. A man borrowed some money from a private organisation at 5% simple interest per annum. He lended this money to another person at 10% compound interest per annum, and made a profit of Rs. 26,410 in 4 years. The man borrowed









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    Let the principal be Rs. P.

    For 4 years, S.I. =
    Principal × Time × Rate
    100

    S.I. =
    P × 4 × 5
    = Rs.
    P
    1005

    C.I. = P 1 +
    R
    T − 1
    100

    C.I. = P 1 +
    10
    4 − 1
    100

    C.I. = P
    11
    4 − 1
    10

    C.I. = P
    14641
    − 1
    10000

    C.I. =
    4641P
    10000

    Correct Option: D

    Let the principal be Rs. P.

    For 4 years, S.I. =
    Principal × Time × Rate
    100

    S.I. =
    P × 4 × 5
    = Rs.
    P
    1005

    C.I. = P 1 +
    R
    T − 1
    100

    C.I. = P 1 +
    10
    4 − 1
    100

    C.I. = P
    11
    4 − 1
    10

    C.I. = P
    14641
    − 1
    10000

    C.I. =
    4641P
    10000

    According to the question,
    ∴ C.I. - S.I. = 26410
    4641P
    P
    = 26410
    100005

    ⇒ 
    4641P − 2000P
    = 2641
    10000

    ⇒ 
    2641P
    = 2641
    10000

    ⇒ P = Rs. 10000


  1. The simple interest on a certain sum of money for 2 years at 5% is Rs. 1600. The compound interest at the same rate after 3 years interest compound annually, is









  1. View Hint View Answer Discuss in Forum

    As we know that ,

    Principal =
    S.I. × 100
    Time × Rate

    Principal =
    1600 × 100
    = Rs. 16000
    5 × 2

    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: B

    As we know that ,

    Principal =
    S.I. × 100
    Time × Rate

    Principal =
    1600 × 100
    = Rs. 16000
    5 × 2

    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
    − 1
    8000

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



  1. The simple interest on a sum of money for 3 years is Rs. 240 and the compound interest on the same sum, at the same rate for 2 years is Rs. 170. The rate of interest is :









  1. View Hint View Answer Discuss in Forum

    As per the given in question ,
    ∵   S.I. for 3 years = Rs. 240

    ∴  S.I. for 2 years =
    240
    × 2 = Rs. 160
    3

    ∴ SI =
    P × R × T
    100

    ∴ 
    PR × 2
    = 160
    100

    ⇒  PR = 160 × 50 = 8000...(i)
    Again, C.I. – S.I. = 170 – 160 = Rs. 10
    ⇒ Difference =
    PR2
    10000

    ⇒ 
    PR2
    = 10
    10000

    Correct Option: C

    As per the given in question ,
    ∵   S.I. for 3 years = Rs. 240

    ∴  S.I. for 2 years =
    240
    × 2 = Rs. 160
    3

    ∴ SI =
    P × R × T
    100

    ∴ 
    PR × 2
    = 160
    100

    ⇒  PR = 160 × 50 = 8000...(i)
    Again, C.I. – S.I. = 170 – 160 = Rs. 10
    ⇒ Difference =
    PR2
    10000

    ⇒ 
    PR2
    = 10
    10000

    ⇒ 
    8000 × R
    = 10
    10000

    ⇒  R =
    100
    =
    25
    = 12
    1
    %
    822


  1. On a certain sum of money, the simple interest for 2 years is Rs. 350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned ?









  1. View Hint View Answer Discuss in Forum

    Time = 2 year , Rate = 4% , S.I. = Rs. 350
    As we know that ,

    Principal =
    S.I. × 100
    Time × Rate

    Principal =
    350 × 100
    = Rs. 4375
    2 × 4

    Difference =
    PR2
    10000

    Correct Option: B

    Time = 2 year , Rate = 4% , S.I. = Rs. 350
    As we know that ,

    Principal =
    S.I. × 100
    Time × Rate

    Principal =
    350 × 100
    = Rs. 4375
    2 × 4

    Difference =
    PR2
    10000

    Difference =
    4375 × 4 × 4
    = Rs. 7
    10000



  1. A certain amount of money earns Rs. 540 as Simple Interest in 3 years. If it earns a Compound Interest of Rs. 376.20 at the same rate of interest in 2 years, find the amount (in Rupees).









  1. View Hint View Answer Discuss in Forum

    Given in question , S.I. for 3 years = Rs. 540

    S.I. for 2 years =
    2
    × 540 = Rs. 360
    3

    C.I. for 2 years = Rs. 376.20
    C.I. – S.I. = 376.20 – 360 = Rs. 16.20
    We have , S.I. for 1 year = Rs. 180
    ∴ Rate of interest =
    16.20
    × 100 = 9% per annum
    180

    ∴  Principal =
    S.I. × 100
    Time × Rate

    Correct Option: C

    Given in question , S.I. for 3 years = Rs. 540

    S.I. for 2 years =
    2
    × 540 = Rs. 360
    3

    C.I. for 2 years = Rs. 376.20
    C.I. – S.I. = 376.20 – 360 = Rs. 16.20
    We have , S.I. for 1 year = Rs. 180
    ∴ Rate of interest =
    16.20
    × 100 = 9% per annum
    180

    ∴  Principal =
    S.I. × 100
    Time × Rate

    Here , Time = 1 year , Rate = 9%
    Principal =
    180 × 100
    = Rs. 2000
    1 × 9