Compound Interest
- The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is ₹ 1.50. The sum is
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Given that , Difference = C.I. - S.I. = ₹ 1.50 , Time = 2 years , Rate = 5%
Using the given formula ,Difference = PR2 10000
Correct Option: A
Given that , Difference = C.I. - S.I. = ₹ 1.50 , Time = 2 years , Rate = 5%
Using the given formula ,Difference = PR2 10000 ⇒ 1.50 = P × 5 × 5 (100)2
⇒ P = 400 × 1.5 = ₹ 600
- On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is ₹ 180. If the rate of interest in both the cases is 10%, then the sum is
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If the interest is compounded half yearly,
Time = 2 years , Rate = 5% half yearly
Using the given formula ,C.I. = P 
1 + R 
T − 1 
100 C.I. = P 1 + 5 2 − 1 100 C.I. = P 21 2 − 1 20 C.I. = 41P 400 S.I. = P × R × T 100 S.I. = P × 10 = P 100 10
According to question ,
∴ C.I. - S.I. = 180⇒ 41P − P = 180 400 10 ⇒ 41 − 40P = 180 400 ⇒ P = 180 400
⇒ P = ₹ 72000
Second Method to solve this question :
Here, C.I. – S.I. = ₹ 180
Interest is compounded half yearly ,R =
10 = 5%, T = 2 years 5 C.I. − S.I. = P 
R 2 100 Correct Option: B
If the interest is compounded half yearly,
Time = 2 years , Rate = 5% half yearly
Using the given formula ,C.I. = P 1 + R T − 1 100 C.I. = P 1 + 5 2 − 1 100 C.I. = P 21 2 − 1 20 C.I. = 41P 400 S.I. = P × R × T 100 S.I. = P × 10 = P 100 10
According to question ,
∴ C.I. - S.I. = 180⇒ 41P − P = 180 400 10 ⇒ 41 − 40P = 180 400 ⇒ P = 180 400
⇒ P = ₹ 72000
Second Method to solve this question :
Here, C.I. – S.I. = ₹ 180
Interest is compounded half yearly ,R =
10 = 5%, T = 2 years 5 C.I. − S.I. = P R 2 100 ⇒ 180 = P 5 2 100
⇒ P = 180 × 20 × 20
P = ₹ 72000
- The difference between simple and compound interests on a sum of money at 4% per annum for 2 years is ₹ 8. The sum is
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Here , Difference = C.I. - S.I. = ₹ 8 , Time = 2 years , Rate = 4%
Let the sum be P.
When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is y, then the sum is given by:Sum = Difference × 100 2 Rate
Correct Option: D
Here , Difference = C.I. - S.I. = ₹ 8 , Time = 2 years , Rate = 4%
Let the sum be P.
When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is y, then the sum is given by:Sum = Difference × 100 2 Rate Sum = ₹ 8 × 100 2 4
Sum = ₹ 8 × 25 × 25 = ₹ 5000
- On what sum does the difference between the compound interest and the simple interest for 3 years at 10% is ₹ 31 ?
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Let the sum be P.
R = 10% , T = 3 years
Using the given formula ,S.I. = P × R × T 100 S.I. = P × 10 × 3 = 3 P 100 10 C.I. = 1 + R T − 1 P 100 C.I. = 1 + 10 3 − 1 P 100 C.I. = 11 3 − 1 P 10 C.I. = 1331 − 1 P = 331 P 1000 1000
∴ C.I. - S.I. = ₹ 31⇒ 331 P − 3 P = 31 1000 10 ⇒ (331 − 300) P = 31 1000 ⇒ 31 P = 31 1000
⇒ P = 1000
∴ Sum = ₹ 1000
We can find required answer with the help of given formula :
Here, C.I. – S.I. = ₹ 31 , R = 10% , T = 3 years , P = ?C.I. − S.I. = P R 2 × 3 + R 100 100
Correct Option: D
Let the sum be P.
R = 10% , T = 3 years
Using the given formula ,S.I. = P × R × T 100 S.I. = P × 10 × 3 = 3 P 100 10 C.I. = 1 + R T − 1 P 100 C.I. = 1 + 10 3 − 1 P 100 C.I. = 11 3 − 1 P 10 C.I. = 1331 − 1 P = 331 P 1000 1000
∴ C.I. - S.I. = ₹ 31⇒ 331 P − 3 P = 31 1000 10 ⇒ (331 − 300) P = 31 1000 ⇒ 31 P = 31 1000
⇒ P = 1000
∴ Sum = ₹ 1000
We can find required answer with the help of given formula :
Here, C.I. – S.I. = ₹ 31 , R = 10% , T = 3 years , P = ?C.I. − S.I. = P R 2 × 3 + R 100 100 31 = P 10 2 × 3 + 10 100 100 31 = P × 1 × 31 100 10
P = ₹ 1000
- On a certain sum of money lent out at 16% p.a. the difference between the compound interest for 1 year, payable half yearly, and the simple interest for 1 year is ₹ 56. The sum is
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As per the given in question ,
Rate of interest = 8% per half year , Time = 2 half years , Difference = C.I. - S.I. = ₹ 56⇒ Difference of interests = PR2 100 ⇒ 56 = P × (8)2 (100)2
Correct Option: C
As per the given in question ,
Rate of interest = 8% per half year , Time = 2 half years , Difference = C.I. - S.I. = ₹ 56⇒ Difference of interests = PR2 100 ⇒ 56 = P × (8)2 (100)2 ⇒ P = 56 × 10000 = ₹ 8750 64
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