Compound Interest

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Aptitude miscellaneous
  1. If the difference between the simple and compound interests on a sum of money for 2 years at 4% per annum is ₹ 80, the sum is :








  1. View Hint View Answer Discuss in Forum

    Here , sum ( P ) = ? , Difference = C.I. - S.I. = ₹ 80 , Rate ( r ) = 40%
    When difference between the compound interest and simple interest on a certain sum of money for 2 years at r % rate is P, then

    Sum = ( C.I. - S.I. )
    100
    		2
    r

    Correct Option: B

    Here , sum ( P ) = ? , Difference = C.I. - S.I. = ₹ 80 , Rate ( r ) = 40%
    When difference between the compound interest and simple interest on a certain sum of money for 2 years at r % rate is P, then

    Sum = ( C.I. - S.I. )
    100
    		2
    r

    ∴  Required sum = 80
    100
    		2
    4

    Required sum = 80 × 25 × 25 = ₹ 50000

  1. The difference between the compound interest (compounded annually) and the simple interest on a sum of ₹ 1000 at a certain rate of interest for 2 years is ₹ 10. The rate of interest per annum is :








  1. View Hint View Answer Discuss in Forum

    Given that , Difference between C.I. and S.I. = ₹ 10 , sum ( P ) = ₹ 1000 , Time = 2 years , Rate = r%
    When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is x, then

    Difference between C.I. and S.I. = Sum
    r
    		2
    100

    ⇒  10 = 1000
    r
    		2
    100

    ⇒ 
    r
    		2 =
    10
    100100

    ⇒ 
    r
    		 = √
    1
    		 =
    1
    10010010

    ⇒  r =
    100
    		 = 10%
    10


    Second Method :
    Here, C.I. – S.I. = Rs. 10, R = ?, T= 2 years, P = Rs. 1000
    C.I. − S.I. = P
    R
    		2
    100

    Correct Option: D

    Given that , Difference between C.I. and S.I. = ₹ 10 , sum ( P ) = ₹ 1000 , Time = 2 years , Rate = r%
    When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is x, then

    Difference between C.I. and S.I. = Sum
    r
    		2
    100

    ⇒  10 = 1000
    r
    		2
    100

    ⇒ 
    r
    		2 =
    10
    100100

    ⇒ 
    r
    		 = √
    1
    		 =
    1
    10010010

    ⇒  r =
    100
    		 = 10%
    10


    Second Method :
    Here, C.I. – S.I. = Rs. 10, R = ?, T= 2 years, P = Rs. 1000
    C.I. − S.I. = P
    R
    		2
    100

    10 = 1000
    R
    		2
    100

    10 = 1000 ×
    R
    		 ×
    R
    100100

    ⇒  R2 = 100
    ⇒  R = √100 = 10%

  1. The difference between compound interest and simple interest on ₹ 2500 for 2 years at 4% per annum is








  1. View Hint View Answer Discuss in Forum

    Here , Principal = ₹ 2500 , Time = 2 years , Rate = 4%
    Using the given formula ,

    S.I. =
    P × R × T
    100

    S.I. = ₹
    2500 × 2 × 4
    		 = ₹ 200
    100

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

    C.I. = ₹ 2500 1 +
    4
    		2 − 1
    100

    C.I. = ₹ 2500
    26
    		2 − 1
    25

    C.I. = ₹
    (676 − 625)
    		 × 2500
    625

    C.I. = ₹
    51
    		 × 2500 = ₹ 204
    625

    ∴  The required difference = C.I. – S.I. = ₹ (204 – 200) = ₹ 4
    Second Method to solve this question :
    Here, C.I. – S.I.= ? , P = ₹ 2500 , R = 4% , T = 2
    C.I. − S.I. = P
    R
    		2
    100

    Correct Option: D

    Here , Principal = ₹ 2500 , Time = 2 years , Rate = 4%
    Using the given formula ,

    S.I. =
    P × R × T
    100

    S.I. = ₹
    2500 × 2 × 4
    		 = ₹ 200
    100

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

    C.I. = ₹ 2500 1 +
    4
    		2 − 1
    100

    C.I. = ₹ 2500
    26
    		2 − 1
    25

    C.I. = ₹
    (676 − 625)
    		 × 2500
    625

    C.I. = ₹
    51
    		 × 2500 = ₹ 204
    625

    ∴  The required difference = C.I. – S.I. = ₹ (204 – 200) = ₹ 4
    Second Method to solve this question :
    Here, C.I. – S.I.= ? , P = ₹ 2500 , R = 4% , T = 2
    C.I. − S.I. = P
    R
    		2
    100

    C.I. – S.I. = 2500
    4
    		2
    100

    C.I. – S.I. = 2500 ×
    1
    		 ×
    1
    2525

    C.I.–S.I. = ₹ 4

  1. If the difference between the compound interest and simple interest on a sum at 5% rate of interest per annum for three years is ₹ 36.60, then the sum is








  1. View Hint View Answer Discuss in Forum

    Given that , Difference = C.I. - S.I.= ₹ 36.60 , Time = 3 years , Rate = 5%
    Using the given formula ,

    Difference of SI and CI for 3 years =
    PR(300 + R)
    1003

    ∵ 
    P × 25 × 305
    		 = 36.60
    100 × 100 × 100

    ⇒  P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    We can find required answer with the help of given formula :
    C.I.–S.I. = ₹ 36.60, R = 5%, P =?, T = 3yrs.
    C.I. − S.I. = P
    R
    		2 × 3 +
    R
    100100

    36.60 = P
    5
    		2 × 3 +
    5
    100100

    36.60 = P ×
    25
    		 ×
    305
    1002100

    P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    P =
    36600000
    		 = ₹ 4800
    25 × 305

    Tricky Approach
    Difference of SI and CI for 3 years =
    PR(300 + R)
    1003

    ∵ 
    P × 25 × 305
    		 = 36.60
    100 × 100 × 100

    ⇒  P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    We can find required answer with the help of given formula :
    C.I.–S.I. = ₹ 36.60, R = 5%, P =?, T = 3yrs.
    C.I. − S.I. = P
    R
    		2 × 3 +
    R
    100100

    Correct Option: D

    Given that , Difference = C.I. - S.I.= ₹ 36.60 , Time = 3 years , Rate = 5%
    Using the given formula ,

    Difference of SI and CI for 3 years =
    PR(300 + R)
    1003

    ∵ 
    P × 25 × 305
    		 = 36.60
    100 × 100 × 100

    ⇒  P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    We can find required answer with the help of given formula :
    C.I.–S.I. = ₹ 36.60, R = 5%, P =?, T = 3yrs.
    C.I. − S.I. = P
    R
    		2 × 3 +
    R
    100100

    36.60 = P
    5
    		2 × 3 +
    5
    100100

    36.60 = P ×
    25
    		 ×
    305
    1002100

    P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    P =
    36600000
    		 = ₹ 4800
    25 × 305

    Tricky Approach
    Difference of SI and CI for 3 years =
    PR(300 + R)
    1003

    ∵ 
    P × 25 × 305
    		 = 36.60
    100 × 100 × 100

    ⇒  P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    We can find required answer with the help of given formula :
    C.I.–S.I. = ₹ 36.60, R = 5%, P =?, T = 3yrs.
    C.I. − S.I. = P
    R
    		2 × 3 +
    R
    100100

    36.60 = P
    5
    		2 × 3 +
    5
    100100

    36.60 = P ×
    25
    		 ×
    305
    1002100

    P =
    36.60 × 100 × 100 × 100
    		 = ₹ 4800
    25 × 305

    P =
    36600000
    		 = ₹ 4800
    25 × 305

  1. The difference between the simple and compound interest on a certain sum of money at 5% rate of interest per annum for 2 years is ₹ 15. Then the sum is :








  1. View Hint View Answer Discuss in Forum

    Here , Difference = C.I. - S.I.= ₹ 15 , Time = 2 years , Rate = 5%
    Let the sum P. Then,

    C.I. = P1 +
    5
    		2 − P
    100

    C.I. =
    441P
    		 − P =
    441x − 400P
    400400

    C.I. =
    41
    		P
    400

    Now,
    S.I. =
    P × 5 × 2
    		 =
    P
    10010

    ∴  (C.I.) – (S.I.) =
    41P
    		−
    P
    40010

    C.I. – S.I. =
    41P − 40P
    		 =
    P
    400400

    ∴ 
    P
    		 = 15
    400

    ⇒  P = 15 × 400 = 6000
    Hence, the sum is ₹ 6000
    Second Method to solve this question :
    C.I. – S.I. = ₹ 15, R = 5%, T = 2 years, P = ?
    C.I. − S.I. = P
    R
    		2
    100

    Correct Option: C

    Here , Difference = C.I. - S.I.= ₹ 15 , Time = 2 years , Rate = 5%
    Let the sum P. Then,

    C.I. = P1 +
    5
    		2 − P
    100

    C.I. =
    441P
    		 − P =
    441x − 400P
    400400

    C.I. =
    41
    		P
    400

    Now,
    S.I. =
    P × 5 × 2
    		 =
    P
    10010

    ∴  (C.I.) – (S.I.) =
    41P
    		−
    P
    40010

    C.I. – S.I. =
    41P − 40P
    		 =
    P
    400400

    ∴ 
    P
    		 = 15
    400

    ⇒  P = 15 × 400 = 6000
    Hence, the sum is ₹ 6000
    Second Method to solve this question :
    C.I. – S.I. = ₹ 15, R = 5%, T = 2 years, P = ?
    C.I. − S.I. = P
    R
    		2
    100

    15 = P
    5
    		2
    100

    P = 15 × 400
    P = ₹ 6000