Compound Interest
- In how many years will a sum of ₹ 800 at 10% per annum compound interest, compounded semi-annually becomes ₹ 926.10 ?
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Here , P = ₹ 800 , A = ₹ 926.10 , Rate = 10% per annum = 5% half yearly
As we know that ,A = P 
1 + R 
T 100 ⇒ 926.10 = 800 1 + 5 T 100 ⇒ 9261 = 21 T 8000 20 ⇒ 21 3 = 21 T 20 20
Correct Option: A
Here , P = ₹ 800 , A = ₹ 926.10 , Rate = 10% per annum = 5% half yearly
As we know that ,A = P 1 + R T 100 ⇒ 926.10 = 800 1 + 5 T 100 ⇒ 9261 = 21 T 8000 20 ⇒ 21 3 = 21 T 20 20 ∴ Time = 3 half years = 1 1 years 2
- At what rate percent per annum will a sum of ₹ 1,000 amounts to ₹ 1,102.50 in 2 years at compound interest ?
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Here , P = ₹ 1,100 , A = ₹ 1,102.50 , T = 2 years
Let rate be 'r '
Using the given formula ,A = P 1 + R T 100 ⇒ 1102.50 = 1 + r 2 1000 100 ⇒ 11025 = 1 + r 2 10000 100 ⇒ 105 2 = 1 + r 2 100 100 ⇒ 1 + r = 105 100 100
Correct Option: A
Here , P = ₹ 1,100 , A = ₹ 1,102.50 , T = 2 years
Let rate be 'r '
Using the given formula ,A = P 1 + R T 100 ⇒ 1102.50 = 1 + r 2 1000 100 ⇒ 11025 = 1 + r 2 10000 100 ⇒ 105 2 = 1 + r 2 100 100 ⇒ 1 + r = 105 100 100 ⇒ r = 5 100 100
⇒ r = 5%
- In what time ₹ 8,000 will amount to ₹ 9,261 at 10% per annum compound interest, when the interest is compounded half yearly ?
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Interest is compounded half yearly.
Given that , P = ₹ 8000 , A = ₹ 9261 , Rate of interest = 5%Let Time = n years or n half-years 2
Using the given formula ,A = P 1 + R T 100 ⇒ 9261 = 8000 1 + 5 n 100 ⇒ 9261 = 21 n 8000 20 ⇒ 21 3 = 21 n 20 20
Correct Option: B
Interest is compounded half yearly.
Given that , P = ₹ 8000 , A = ₹ 9261 , Rate of interest = 5%Let Time = n years or n half-years 2
Using the given formula ,A = P 1 + R T 100 ⇒ 9261 = 8000 1 + 5 n 100 ⇒ 9261 = 21 n 8000 20 ⇒ 21 3 = 21 n 20 20 ⇒ n = 3 half years = 3 years = 1 1 years 2 2
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when the interest being compounded annually, isThe compound interest on ₹ 6,000 at 10% per annum for 1 1 years, 2
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Here , A = ? , P = ₹ 6,000 , R = 10% , T = ( 3 / 2 ) years
Amount = 6000 1 + 10 × 1 + (1/2) × 10 100 100 ⇒ Amount = 6000 × 11 × 21 = ₹ 6930 10 20
Second Method to solve this question :
Here, t = nFA = P 1 + r n 1 + rF 100 100
Correct Option: C
Here , A = ? , P = ₹ 6,000 , R = 10% , T = ( 3 / 2 ) years
Amount = 6000 1 + 10 × 1 + (1/2) × 10 100 100 ⇒ Amount = 6000 × 11 × 21 = ₹ 6930 10 20
Second Method to solve this question :
Here, t = nFA = P 1 + r n 1 + rF 100 100
∴ A = ₹ 6930
CI = Amount - Principal
∴ CI = ₹ (6930 – 6000) = ₹ 930
- The sum of money that yields a compound interest of ₹ 420 during the second year at 5% p.a is
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Here , Compound Interest ( CI ) = ₹ 420 , Rate ( R ) = 5% , Time = 2 years
As we know that ,CI = P 
1 + R T − 1 
− PR 100 100 ⇒ 420 = P 1 + 5 2 − 1 − P × 5 100 100 ⇒ 420 = P 21 2 − 1 − 5P 20 100 ⇒ 420 = P 441 − 1 − 5P 400 100 ⇒ 420 = P 441 - 400 − 5P 400 100
Correct Option: C
Here , Compound Interest ( CI ) = ₹ 420 , Rate ( R ) = 5% , Time = 2 years
As we know that ,CI = P 1 + R T − 1 − PR 100 100 ⇒ 420 = P 1 + 5 2 − 1 − P × 5 100 100 ⇒ 420 = P 21 2 − 1 − 5P 20 100 ⇒ 420 = P 441 − 1 − 5P 400 100 ⇒ 420 = P 441 - 400 − 5P 400 100 ⇒ 420 = 41P − 5P = 21P 400 100 400 ⇒ P = 420 × 400 = ₹ 8000 21
