Compound Interest
- A principal of ₹ 10,000, after 2 years compounded annually, the rate of interest being 10% per annum during the first year and 12% per annum during the second year (in rupees) will amount to :
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Given that , Principal ( P ) = ₹ 10,000, Time = 2 years , r1 = 10% , r2 = 12%
Using the given formula,A = P 
1 + r1 
. 1 + r2 100 100 A = 10000 1 + 10 . 1 + 12 100 100 A = 10000 1 + 1 . 1 + 3 10 25
Correct Option: B
Given that , Principal ( P ) = ₹ 10,000, Time = 2 years , r1 = 10% , r2 = 12%
Using the given formula,A = P 1 + r1 . 1 + r2 100 100 A = 10000 1 + 10 . 1 + 12 100 100 A = 10000 1 + 1 . 1 + 3 10 25 ⇒ A = 10000 × 11 × 28 = ₹ 12320 10 25
- A sum of ₹ 8000 will amount to ₹ 8820 in 2 years if the interest is calculated every year. The rate of compound interest is
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Here , Principal ( P ) = ₹ 8,000 , Amount ( A ) = ₹ 8820 , Rate ( R ) = r% , Time = 2 years
If the rate of C.I. be r% per annum, thenA = P 1 + R T 100 ⇒ 8820 = 8000 1 + r 2 100 ⇒ 8820 = 1 + r 2 8000 100 ⇒ 441 = 21 2 = 1 + r 2 400 20 100 ⇒ 1 + r = 21 100 20
Correct Option: D
Here , Principal ( P ) = ₹ 8,000 , Amount ( A ) = ₹ 8820 , Rate ( R ) = r% , Time = 2 years
If the rate of C.I. be r% per annum, thenA = P 1 + R T 100 ⇒ 8820 = 8000 1 + r 2 100 ⇒ 8820 = 1 + r 2 8000 100 ⇒ 441 = 21 2 = 1 + r 2 400 20 100 ⇒ 1 + r = 21 100 20 ⇒ r = 21 − 1 = 1 100 20 20 ⇒ r = 1 × 100 20
∴ r = 5% per annum
- The compound interest on ₹ 30,000 at 7% per annum for a certain time is ₹ 4,347. The time is
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Here , Principal ( P ) = ₹ 30,000 , Compound Interest ( CI ) = ₹ 4347 , Rate ( R ) = 7% , Time = T
Amount ( A ) = Principal + CI = 30000 + 4347 = ₹ 34347A = P 1 + R T 100 ⇒ 34347 = 30000 1 + 7 T 100 ⇒ 34347 = 107 T 30000 100
Correct Option: C
Here , Principal ( P ) = ₹ 30,000 , Compound Interest ( CI ) = ₹ 4347 , Rate ( R ) = 7% , Time = T
Amount ( A ) = Principal + CI = 30000 + 4347 = ₹ 34347A = P 1 + R T 100 ⇒ 34347 = 30000 1 + 7 T 100 ⇒ 34347 = 107 T 30000 100 ⇒ 11449 = 107 2 = 107 T 10000 100 100
Equating powers on both sides ,
⇒ Time = 2 years
- In what time will ₹ 1000 amounts to ₹ 1331 at 20% per annum, compounded half yearly ?
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Given that , P = ₹ 1000 , A = ₹ 1331
Let the required time be t years.
Interest is compounded half yearly
∴ Time = 2t half yearsand rate = 20 = 10% 2 ∴ 1000 1 + 10 2t = 1331 100 ⇒ 11 2t = 1331 10 1000 ⇒ 11 2t = 11 3 ⇒2t = 3 10 10
Correct Option: A
Given that , P = ₹ 1000 , A = ₹ 1331
Let the required time be t years.
Interest is compounded half yearly
∴ Time = 2t half yearsand rate = 20 = 10% 2 ∴ 1000 1 + 10 2t = 1331 100 ⇒ 11 2t = 1331 10 1000 ⇒ 11 2t = 11 3 ⇒2t = 3 10 10 ∴ t =
3 years or 1 1 years 2 2
- An amount of ₹ 6,000 lent at 5% per annum compound interest for 2 years will become
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Here , P = ₹ 6000 , A = ? , R = 5%, T = 2 years
Using the given formula ,A = P 1 + R T 100 A = 6000 1 + 5 2 100
Correct Option: D
Here , P = ₹ 6000 , A = ? , R = 5%, T = 2 years
Using the given formula ,A = P 1 + R T 100 A = 6000 1 + 5 2 100 ⇒ A = 6000 × 21 × 21 = ₹ 6615 20 20
