Compound Interest


  1. A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is :









  1. View Hint View Answer Discuss in Forum

    Let principal be P.
    Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
    Using the given formula , we have

    A = P1 +
    R
    T
    100

    ⇒ 800 = P 1 +
    R
    3  ....(i)
    100

    and,
    840 = P 1 +
    R
    4  ....(ii)
    100

    On dividing equation (ii) by (i),
    840
    = 1 +
    R
    800100

    ⇒ 
    21
    = 1 +
    R
    20100

    Correct Option: C

    Let principal be P.
    Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
    Using the given formula , we have

    A = P1 +
    R
    T
    100

    ⇒ 800 = P 1 +
    R
    3  ....(i)
    100

    and,
    840 = P 1 +
    R
    4  ....(ii)
    100

    On dividing equation (ii) by (i),
    840
    = 1 +
    R
    800100

    ⇒ 
    21
    = 1 +
    R
    20100

    ⇒ 
    R
    =
    21
    − 1 =
    1
    1002020

    ⇒  R =
    1
    × 100 = 5% per annum
    20


  1. The compound interest on a sum of Rs. 5000 at 8% per annum for 9 months when interest is compound quarterly is :









  1. View Hint View Answer Discuss in Forum

    When interest is compound quarterly ,

    Rate of interest =
    8
    = 2% per quarter , Time = 3 quarters
    4

    Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
    We can find required answer with the help of given formula ,
    C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 5000 1 +
    2
    3 − 1
    100

    Correct Option: C

    When interest is compound quarterly ,

    Rate of interest =
    8
    = 2% per quarter , Time = 3 quarters
    4

    Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
    We can find required answer with the help of given formula ,
    C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 5000 1 +
    2
    3 − 1
    100

    C.I. = 5000[(1.02)3 - 1]
    C.I. = 5000 (1.061208 – 1)
    C.I. = 5000 × 0.061208 = Rs. 306.04



  1. A sum of Rs. 2420 is accumulated in 2 years at 10% compund interest on a certain amount. Then the original amount is :









  1. View Hint View Answer Discuss in Forum

    Let the principal be Rs. P.
    Given in question , Amount ( A ) = Rs. 2420 , Rate ( R ) = 10% , Time = 2 years
    Using the given formula ,

    ∴ A = P1 +
    R
    T
    100

    ⇒  2420 = P1 +
    10
    2
    100

    ⇒  2420 = P × 1 +
    10
    2
    100

    ⇒  2420 = P
    11
    2
    10

    Correct Option: B

    Let the principal be Rs. P.
    Given in question , Amount ( A ) = Rs. 2420 , Rate ( R ) = 10% , Time = 2 years
    Using the given formula ,

    ∴ A = P1 +
    R
    T
    100

    ⇒  2420 = P1 +
    10
    2
    100

    ⇒  2420 = P × 1 +
    10
    2
    100

    ⇒  2420 = P
    11
    2
    10

    ⇒  P =
    2420 × 10 × 10
    = Rs. 2000
    11 × 11


  1. The compound interest on Rs. 30,000 at 7% per annum for n years is Rs. 4347. The value of n is









  1. View Hint View Answer Discuss in Forum

    Here , Principal = Rs. 30000 , CI = Rs. 4347 , Rate = 7% , Time = n years
    Amount = Principal + CI = Rs. (30000 + 4347) = Rs. 34347
    Using the given formula ,

    A = P1 +
    R
    T
    100

    ⇒  34347 = 300001 +
    7
    n
    100

    ⇒ 
    34347
    =
    107
    n
    30000100

    ⇒ 
    11449
    =
    107
    n
    10000100

    Correct Option: B

    Here , Principal = Rs. 30000 , CI = Rs. 4347 , Rate = 7% , Time = n years
    Amount = Principal + CI = Rs. (30000 + 4347) = Rs. 34347
    Using the given formula ,

    A = P1 +
    R
    T
    100

    ⇒  34347 = 300001 +
    7
    n
    100

    ⇒ 
    34347
    =
    107
    n
    30000100

    ⇒ 
    11449
    =
    107
    n
    10000100

    ⇒ 
    107
    2 =
    107
    n
    100100

    On equating powers both sides ,
    ⇒  n = 2 years



  1. The compound interest on Rs. 12000 for 9 months at 20% per annum, interest being compounded quarterly is :









  1. View Hint View Answer Discuss in Forum

    Given that , P = Rs. 12000 , Rate of interest =
    20
    = 5% per quarter , Time = 3 quarters
    4

    We can find required answer with the help of given formula ,
    ∴  C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 12000 1 +
    5
    3 − 1
    100

    C.I. = 12000 1 +
    1
    3 − 1
    20

    C.I. = 12000
    21
    3 − 1
    20

    C.I. = 12000
    9261
    − 1
    8000

    Correct Option: C

    Given that , P = Rs. 12000 , Rate of interest =
    20
    = 5% per quarter , Time = 3 quarters
    4

    We can find required answer with the help of given formula ,
    ∴  C.I. = P 1 +
    R
    T − 1
    100

    C.I. = 12000 1 +
    5
    3 − 1
    100

    C.I. = 12000 1 +
    1
    3 − 1
    20

    C.I. = 12000
    21
    3 − 1
    20

    C.I. = 12000
    9261
    − 1
    8000

    C.I. = 12000
    9261 - 8000
    8000

    ∴ C.I. =
    12000 × 1261
    = Rs. 1891.5
    8000