Compound Interest
- If the compound interest on a certain sum for 2 years at 4% p.a. is ₹ 102, the simple interest at the same rate of interest for two years would be
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Here , Compound Interest ( CI ) = ₹ 102 , Rate ( R ) = 4% , Time = 2 years
If the sum ( Principal ) be P, thenC.I. = P 
1 + R 
T − 1 
100 ⇒ 102 = P 1 + 4 2 − 1 100 ⇒ 102 = P 26 2 − 1 25 ⇒ 102 = P 
676 − 1 625 ⇒ 102 = P 676 − 625 625
Correct Option: D
Here , Compound Interest ( CI ) = ₹ 102 , Rate ( R ) = 4% , Time = 2 years
If the sum ( Principal ) be P, thenC.I. = P 1 + R T − 1 100 ⇒ 102 = P 1 + 4 2 − 1 100 ⇒ 102 = P 26 2 − 1 25 ⇒ 102 = P 676 − 1 625 ⇒ 102 = P 676 − 625 625 ⇒ 102 = P × 51 625 ⇒ P = 102 × 625 = ₹ 1250 51 ∴ S.I.= 1250 × 2 × 4 = ₹ 100 100
- What sum will give ₹ 244 as the difference between simple interest and compound interest
at 10% in 1 1 years compounded half yearly ? 2
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If Interest is compounded half yearly ,
Time = 3 years 2 ⇒ Time = 3 × 2 = 3 half years 2 Rate = 10 = 5% per half year , Difference = C.I. - S.I. = ₹ 244 2
[∵ when r → r/2, then t → 2t]
Using the given formula ,Difference = P r3 + 3r2 1000000 10000 ⇒ 244 = P 125 + 75 1000000 10000 ⇒ 244 = P 125 + 7500 1000000
Correct Option: C
If Interest is compounded half yearly ,
Time = 3 years 2 ⇒ Time = 3 × 2 = 3 half years 2 Rate = 10 = 5% per half year , Difference = C.I. - S.I. = ₹ 244 2
[∵ when r → r/2, then t → 2t]
Using the given formula ,Difference = P r3 + 3r2 1000000 10000 ⇒ 244 = P 125 + 75 1000000 10000 ⇒ 244 = P 125 + 7500 1000000 ⇒ 244 = P 7625 1000000 ⇒ P = 244 × 1000000 = ₹ 32000 7625
- The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is
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Given in question , Principal = Rs. 15,000 , C.I. - S.I. = Rs. 96 , Time = 2 years , Rate = R%
For 2 years,C.I. – S.I. = PR2 10000 ⇒ 96 = 15000 × R2 10000
Correct Option: C
Given in question , Principal = Rs. 15,000 , C.I. - S.I. = Rs. 96 , Time = 2 years , Rate = R%
For 2 years,C.I. – S.I. = PR2 10000 ⇒ 96 = 15000 × R2 10000
⇒ 15 R2 = 960⇒ R2 = 960 = 64 15
⇒ R = √64 = 8% per annum
- The difference between the simple interest and compound interest (compounded annually) on Rs. 40,000 for 3 years at 8% per annum is :
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Here , Principal = Rs. 40,000 , C.I. - S.I. = ? , Time = 3 years , Rate = 8%
Difference between C.I. and S.I. for 3 years = P r 2 r + 3 100 100 C.I. - S.I. = 40000 8 2 8 + 3 100 100 C.I. - S.I. = 40000 × 64 8 + 300 10000 100
Correct Option: B
Here , Principal = Rs. 40,000 , C.I. - S.I. = ? , Time = 3 years , Rate = 8%
Difference between C.I. and S.I. for 3 years = P r 2 r + 3 100 100 C.I. - S.I. = 40000 8 2 8 + 3 100 100 C.I. - S.I. = 40000 × 64 8 + 300 10000 100 C.I. - S.I. = 4 × 64 × 308 = 78848 100 100
∴ C.I. - S.I. = Rs. 788.48
- If the difference of the compound interest and the simple interest on a sum of money for 3 years is Rs. 186. Find the sum of money, if the rate of interest in both cases be 10%.
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Given in question , C.I. - S.I. = Rs. 186 , Time = 3 years , Rate = 10%
Using the given formula ,For 3 years , C.I. − S.I. = P r 2 r + 3 100 100 ⇒ P 10 2 10 + 3 = 186 100 100
Correct Option: D
Given in question , C.I. - S.I. = Rs. 186 , Time = 3 years , Rate = 10%
Using the given formula ,For 3 years , C.I. − S.I. = P r 2 r + 3 100 100 ⇒ P 10 2 10 + 3 = 186 100 100 ⇒ P 1 × 31 = 186 100 10 ⇒ P = 186 × 1000 = Rs. 6000 31
