Compound Interest
 A sum becomes ₹ 1,352 in 2 years at 4% per annum compound interest. The sum is

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Let the sum be ₹ p.
Here , A = ₹ 1352 , r = 4% , n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 ∴ 1352 = p 1 + 4 ^{2} 100 ⇒ 1352 = p 1 + 1 ^{2} 25
Correct Option: D
Let the sum be ₹ p.
Here , A = ₹ 1352 , r = 4% , n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 ∴ 1352 = p 1 + 4 ^{2} 100 ⇒ 1352 = p 1 + 1 ^{2} 25 ⇒ 1352 = p 26 ^{2} 25 ⇒ p = 1352 × 25 × 25 = ₹ 1250 26 × 26
 At what rate percent per annum will ₹ 2304 amount to ₹ 2500 in 2 years at compound interest ?

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Let the rate percent per annum be r.
Given that , P = ₹ 2304 , A = ₹ 2500 , n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 2500 = 2304 1 + r ^{2} 100 ⇒ 1 + r ^{2} = 2500 = 50 ^{2} 100 2304 48 ⇒ 1 + r = 50 = 25 100 48 24 ⇒ r = 25 − 1 = 1 100 24 24
Correct Option: C
Let the rate percent per annum be r.
Given that , P = ₹ 2304 , A = ₹ 2500 , n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 2500 = 2304 1 + r ^{2} 100 ⇒ 1 + r ^{2} = 2500 = 50 ^{2} 100 2304 48 ⇒ 1 + r = 50 = 25 100 48 24 ⇒ r = 25 − 1 = 1 100 24 24 ⇒ r = 100 = 25 = 4 1 % 24 6 6
 A sum of money on compound interest amounts to ₹ 10648 in 3 years and ₹ 9680 in 2 years. The rate of interest per annum is :

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Let the sum be ₹ P and rate of interest be R% per annum.
Here , A_{1} = ₹ 10648 , A_{2} = ₹ 9680
and t_{1} = 3 years , t_{2} = 2 years
Using the given formula ,A = P 1 + R ^{n} 100
Then,P 1 + R ^{2} = 9680 ...(i) 100 P 1 + R ^{3} = 10648 ...(ii) 100
On dividing equation (ii) by (i)1 + R = 10648 100 9680 ⇒ R = 10648 − 1 100 9680 = 10648 − 9680 9680
Correct Option: B
Let the sum be ₹ P and rate of interest be R% per annum.
Here , A_{1} = ₹ 10648 , A_{2} = ₹ 9680
and t_{1} = 3 years , t_{2} = 2 years
Using the given formula ,A = P 1 + R ^{n} 100
Then,P 1 + R ^{2} = 9680 ...(i) 100 P 1 + R ^{3} = 10648 ...(ii) 100
On dividing equation (ii) by (i)1 + R = 10648 100 9680 ⇒ R = 10648 − 1 100 9680 = 10648 − 9680 9680 ⇒ R = 968 = 1 100 9680 10 ⇒ R = 1 × 100 = 10% 10
 The principal, which will amount to ₹ 270.40 in 2 years at the rate of 4% per annum compound interest, is

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Let the principal be ₹ P.
Here , A = ₹ 270.40 , r = 4%, n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 ∴ 270.40 = P 1 + 4 ^{2} 100
⇒ 270.40 = P (1 + 0.04)^{2}
Correct Option: C
Let the principal be ₹ P.
Here , A = ₹ 270.40 , r = 4%, n = 2 years
Using the given formula ,A = P 1 + r ^{n} 100 ∴ 270.40 = P 1 + 4 ^{2} 100
⇒ 270.40 = P (1 + 0.04)^{2}⇒ P = 270.40 = ₹ 250 1.04 × 1.04
 In what time will ₹ 1000 becomes ₹ 1331 at 10% per annum compounded annually ?

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Here , P = ₹ 1000, P_{1} = ₹ 1331 , r = 10%
Let the required time be n years. Then,
Using the given formula ,∴ P_{1} = P 1 + r ^{n} 100 1331 = 1000 1 + 10 ^{n} 100 ⇒ 1331 = 10 + 1 ^{n} 1000 10
Correct Option: A
Here , P = ₹ 1000, P_{1} = ₹ 1331 , r = 10%
Let the required time be n years. Then,
Using the given formula ,∴ P_{1} = P 1 + r ^{n} 100 1331 = 1000 1 + 10 ^{n} 100 ⇒ 1331 = 10 + 1 ^{n} 1000 10 ⇒ 11 ^{n} = 11 ^{3} 10 10
Equating on both sides , we get
⇒ n = 3