Compound Interest
- In how many years will a sum of Rs. 800 at 10% per annum compounded semi-annually become Rs. 926.10?
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According to question ,
Rate = 10% Per annum = 5% per half year , Time = T years = 2T half years
We can find required answer with the help of given formula ,∴ A = P 
1 + R 
T 100 ⇒ 926.10 = 800 1 + 5 2T 100 ⇒ 926.1 = 
1 + 1 2T 800 20 ⇒ 9261 = 21 2T 8000 20
Correct Option: D
According to question ,
Rate = 10% Per annum = 5% per half year , Time = T years = 2T half years
We can find required answer with the help of given formula ,∴ A = P 1 + R T 100 ⇒ 926.10 = 800 1 + 5 2T 100 ⇒ 926.1 = 1 + 1 2T 800 20 ⇒ 9261 = 21 2T 8000 20 ⇒ 21 3 = 21 2T 20 20
Equating powers on both sides , we get⇒ 2T = 3 ⇒ T = 3 years 2
- A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years will the same amount become Rs. 8000 ?
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Here , Amount ( A ) = Rs. 4000 , P = Rs. 2000 , Rate = R% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 4000 = 2000 1 + R 2 100 ⇒ 2 = 1 + R 2 100 ⇒ 1 + R = √2 ......(1) 100
Again , Amount ( A ) = Rs. 8000 , P = Rs. 2000 , Rate = R% , Time = ?∴ 8000 = 2000 1 + R T 100
Correct Option: B
Here , Amount ( A ) = Rs. 4000 , P = Rs. 2000 , Rate = R% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 4000 = 2000 1 + R 2 100 ⇒ 2 = 1 + R 2 100 ⇒ 1 + R = √2 ......(1) 100
Again , Amount ( A ) = Rs. 8000 , P = Rs. 2000 , Rate = R% , Time = ?∴ 8000 = 2000 1 + R T 100
⇒ 4 = (√2)T { Using (1) }
⇒ (√2)4 = (√2)T
⇒ T = 4 years
- Find the amount which Shyam will get on Rs. 4096, if he gives it for
18 months at 12 1 % per annum, interest being compounded half yearly. 2
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When interest is compounded half yearly ,
Principal = Rs. 4096 , Time = 3 years = 3 half years 2 Rate = 25 % per annum = 25 per half year 2 4
Using the given formula ,∴ A = P 1 + R T 100 A = 4096 1 + 25 3 400 A = 4096 1 + 1 3 16
Correct Option: C
When interest is compounded half yearly ,
Principal = Rs. 4096 , Time = 3 years = 3 half years 2 Rate = 25 % per annum = 25 per half year 2 4
Using the given formula ,∴ A = P 1 + R T 100 A = 4096 1 + 25 3 400 A = 4096 1 + 1 3 16 A = 4096 × 17 × 17 × 17 = Rs. 4913 16 16 16
- If Rs. 10000 amounts to Rs. 11664 invested in compound interest (compounded annually) for two years then the annual rate of compound interest is
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Given that , Amount ( A ) = Rs. 11664 , P = Rs. 10000 , Rate = R% , Time = 2 years
We can find required answer with the help of given formula ,A = P 1 + R T 100 ⇒ 11664 = 10000 1 + R 2 100 ⇒ 11664 = 1 + R 2 10000 100 ⇒ 108 2 = 1 + R 2 100 100 ⇒ 1 + R = 108 100 100 ⇒ R = 108 − 1 = 8 100 100 100
Correct Option: C
Given that , Amount ( A ) = Rs. 11664 , P = Rs. 10000 , Rate = R% , Time = 2 years
We can find required answer with the help of given formula ,A = P 1 + R T 100 ⇒ 11664 = 10000 1 + R 2 100 ⇒ 11664 = 1 + R 2 10000 100 ⇒ 108 2 = 1 + R 2 100 100 ⇒ 1 + R = 108 100 100 ⇒ R = 108 − 1 = 8 100 100 100 ∴ R = 8 × 100 100
R = 8% per annum
- The compound interest on Rs. 4000 for 4 years at 10% per annum will be
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Here , Principal ( P ) = Rs. 4000 , Compound Interest ( CI ) = ? , Rate ( R ) = 10% , Time = 4 years
Using the given formula ,C.I. = P 
1 + R T − 1 
100 C.I. = 4000 1 + 10 4 − 1 100
Correct Option: A
Here , Principal ( P ) = Rs. 4000 , Compound Interest ( CI ) = ? , Rate ( R ) = 10% , Time = 4 years
Using the given formula ,C.I. = P 1 + R T − 1 100 C.I. = 4000 1 + 10 4 − 1 100 C.I. = 4000 11 4 − 1 10
C.I. = 4000 (1.4641 – 1)
∴ C.I. = 4000 × 0.4641 = Rs. 1856.4
