Compound Interest
- A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum.
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Given that , A1 = Rs. 2420 , T1 = 2 years and A2 = Rs. 2662 , T2 = 3 years
A = P 
1 + R 
T 100 ∴ 2420 = P 1 + R 2 .... (i) 100 and, 2662 = P 1 + R 3 .... (ii) 100
By equation (ii) ÷ (i)2662 = 1 + R 2420 100 ⇒ R = 2662 − 1 100 2420 ⇒ R = 2662 - 2420 100 2420 ⇒ R = 242 = 1 100 2420 10
⇒ R = 10% per annum.
From equation (i),2420 = P 1 + 10 2 100
Correct Option: B
Given that , A1 = Rs. 2420 , T1 = 2 years and A2 = Rs. 2662 , T2 = 3 years
A = P 1 + R T 100 ∴ 2420 = P 1 + R 2 .... (i) 100 and, 2662 = P 1 + R 3 .... (ii) 100
By equation (ii) ÷ (i)2662 = 1 + R 2420 100 ⇒ R = 2662 − 1 100 2420 ⇒ R = 2662 - 2420 100 2420 ⇒ R = 242 = 1 100 2420 10
⇒ R = 10% per annum.
From equation (i),2420 = P 1 + 10 2 100 ⇒ 2420 = P 11 2 10 ⇒ 2420 = P × 121 100 ⇒ P = 2420 × 100 = Rs. 2000 121
- A sum of Rs. 3000 amounts to Rs. 6000 in two years at compound interest. The interest for four years is :
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Given in question , Amount ( A ) = Rs. 6000 , P = Rs. 3000 , Rate = R% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 6000 = 3000 1 + R 2 100 ⇒ 2 = 1 + R 2 100
On squaring both sides , we get4 = 1 + R 4 100
Again , Amount ( A ) = ? , P = Rs. 3000 , Rate = R% , Time = 4 years
Correct Option: A
Given in question , Amount ( A ) = Rs. 6000 , P = Rs. 3000 , Rate = R% , Time = 2 years
Using the given formula ,A = P 1 + R T 100 ⇒ 6000 = 3000 1 + R 2 100 ⇒ 2 = 1 + R 2 100
On squaring both sides , we get4 = 1 + R 4 100
Again , Amount ( A ) = ? , P = Rs. 3000 , Rate = R% , Time = 4 years⇒ A = 3000 1 + R 4 100
Amount = Rs. (4 × 3000) = Rs. 12000
∴ C.I. = Amount - Principal
∴ C.I. = Rs. (12000 – 3000) = Rs. 9000
- If a sum of Rs. 12500 is invested for 1 year at 12% per annum interest being compounded semiannually, then interest earned is :
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If interest is compounded semiannually , then
Rate of interest = 12% per annum = 6% per half–year , Time = 2 half years
Here , P = Rs. 12500∴ C.I. = P 
1 + R T − 1 
100 C.I. = 12500 1 + 6 2 − 1 100 C.I. = 12500 1 + 3 2 − 1 50 C.I. = 12500 53 2 − 1 50 C.I. = 12500 2809 − 1 2500
Correct Option: C
If interest is compounded semiannually , then
Rate of interest = 12% per annum = 6% per half–year , Time = 2 half years
Here , P = Rs. 12500∴ C.I. = P 1 + R T − 1 100 C.I. = 12500 1 + 6 2 − 1 100 C.I. = 12500 1 + 3 2 − 1 50 C.I. = 12500 53 2 − 1 50 C.I. = 12500 2809 − 1 2500 C.I. = 12500 2809 - 2500 2500 C.I. = Rs. 12500 × 309 2500
∴ C.I. = Rs. 1545
- A sum of money amounts to Rs. 6655 at the rate of 10% compounded annually for 3 years. The sum of money is
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Let the principal be Rs. P.
Here , Amount ( A ) = Rs. 6655 , P = ? , Rate = 10% , Time = 3 years
Using the given formula , we haveA = P 1 + R T 100 ⇒ 6655 = P 1 + 10 3 100 ⇒ 6655 = P 1 + 1 3 10
Correct Option: A
Let the principal be Rs. P.
Here , Amount ( A ) = Rs. 6655 , P = ? , Rate = 10% , Time = 3 years
Using the given formula , we haveA = P 1 + R T 100 ⇒ 6655 = P 1 + 10 3 100 ⇒ 6655 = P 1 + 1 3 10 ⇒ 6655 = P 11 3 10 ⇒ P = 6655 × 10 × 10 × 10 = Rs. 5000 11 × 11 × 11
- In what time (in years) will Rs. 8000 amount to Rs. 9261 at 5% per annum, compounded annually?
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Let the time be T years.
Given that , Amount ( A ) = Rs. 9261 , P = Rs. 8000 , Rate = 5%
We can find required answer with the help of given formula ,∴ A = P 1 + R T 100 ⇒ 9261 = 8000 1 + 5 T 100 ⇒ 9261 = 1 + 1 T 8000 20
Correct Option: A
Let the time be T years.
Given that , Amount ( A ) = Rs. 9261 , P = Rs. 8000 , Rate = 5%
We can find required answer with the help of given formula ,∴ A = P 1 + R T 100 ⇒ 9261 = 8000 1 + 5 T 100 ⇒ 9261 = 1 + 1 T 8000 20 ⇒ 21 3 = 21 T 20 20
On equating powers both sides , we get
⇒ T = 3 years
