Compound Interest
- A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is :
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Let principal be P.
Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
Using the given formula , we haveA = P 1 + R T 100 ⇒ 800 = P 1 + R 3 ....(i) 100
and,840 = P 1 + R 4 ....(ii) 100
On dividing equation (ii) by (i),840 = 1 + R 800 100 ⇒ 21 = 1 + R 20 100
Correct Option: C
Let principal be P.
Given that , A1 = Rs. 800 , T1 = 3 years and A2 = Rs. 840 , T2 = 4 years , R1 = R2 = R%
Using the given formula , we haveA = P 1 + R T 100 ⇒ 800 = P 1 + R 3 ....(i) 100
and,840 = P 1 + R 4 ....(ii) 100
On dividing equation (ii) by (i),840 = 1 + R 800 100 ⇒ 21 = 1 + R 20 100 ⇒ R = 21 − 1 = 1 100 20 20 ⇒ R = 1 × 100 = 5% per annum 20
- The compound interest on a sum of Rs. 5000 at 8% per annum for 9 months when interest is compound quarterly is :
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When interest is compound quarterly ,
Rate of interest = 8 = 2% per quarter , Time = 3 quarters 4
Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
We can find required answer with the help of given formula ,C.I. = P 1 + R T − 1 100 C.I. = 5000 1 + 2 3 − 1 100
Correct Option: C
When interest is compound quarterly ,
Rate of interest = 8 = 2% per quarter , Time = 3 quarters 4
Here , Principal ( P ) = ₹ 5,000 , Compound Interest ( CI ) = ?
We can find required answer with the help of given formula ,C.I. = P 1 + R T − 1 100 C.I. = 5000 1 + 2 3 − 1 100
C.I. = 5000[(1.02)3 - 1]
C.I. = 5000 (1.061208 – 1)
C.I. = 5000 × 0.061208 = Rs. 306.04
- A sum of Rs. 2420 is accumulated in 2 years at 10% compund interest on a certain amount. Then the original amount is :
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Let the principal be Rs. P.
Given in question , Amount ( A ) = Rs. 2420 , Rate ( R ) = 10% , Time = 2 years
Using the given formula ,∴ A = P 1 + R T 100 ⇒ 2420 = P 1 + 10 2 100 ⇒ 2420 = P × 1 + 10 2 100 ⇒ 2420 = P 11 2 10
Correct Option: B
Let the principal be Rs. P.
Given in question , Amount ( A ) = Rs. 2420 , Rate ( R ) = 10% , Time = 2 years
Using the given formula ,∴ A = P 1 + R T 100 ⇒ 2420 = P 1 + 10 2 100 ⇒ 2420 = P × 1 + 10 2 100 ⇒ 2420 = P 11 2 10 ⇒ P = 2420 × 10 × 10 = Rs. 2000 11 × 11
- The compound interest on Rs. 30,000 at 7% per annum for n years is Rs. 4347. The value of n is
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Here , Principal = Rs. 30000 , CI = Rs. 4347 , Rate = 7% , Time = n years
Amount = Principal + CI = Rs. (30000 + 4347) = Rs. 34347
Using the given formula ,A = P 1 + R T 100 ⇒ 34347 = 30000 1 + 7 n 100 ⇒ 34347 = 107 n 30000 100 ⇒ 11449 = 107 n 10000 100
Correct Option: B
Here , Principal = Rs. 30000 , CI = Rs. 4347 , Rate = 7% , Time = n years
Amount = Principal + CI = Rs. (30000 + 4347) = Rs. 34347
Using the given formula ,A = P 1 + R T 100 ⇒ 34347 = 30000 1 + 7 n 100 ⇒ 34347 = 107 n 30000 100 ⇒ 11449 = 107 n 10000 100 ⇒ 107 2 = 107 n 100 100
On equating powers both sides ,
⇒ n = 2 years
- The compound interest on Rs. 12000 for 9 months at 20% per annum, interest being compounded quarterly is :
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Given that , P = Rs. 12000 , Rate of interest = 20 = 5% per quarter , Time = 3 quarters 4
We can find required answer with the help of given formula ,∴ C.I. = P 1 + R T − 1 100 C.I. = 12000 1 + 5 3 − 1 100 C.I. = 12000 1 + 1 3 − 1 20 C.I. = 12000 21 3 − 1 20 C.I. = 12000 9261 − 1 8000
Correct Option: C
Given that , P = Rs. 12000 , Rate of interest = 20 = 5% per quarter , Time = 3 quarters 4
We can find required answer with the help of given formula ,∴ C.I. = P 1 + R T − 1 100 C.I. = 12000 1 + 5 3 − 1 100 C.I. = 12000 1 + 1 3 − 1 20 C.I. = 12000 21 3 − 1 20 C.I. = 12000 9261 − 1 8000 C.I. = 12000 9261 - 8000 8000 ∴ C.I. = 12000 × 1261 = Rs. 1891.5 8000