Compound Interest
- A certain sum, invested at 4% per annum compound interest, compounded halfyearly, amounts to ₹ 7,803 at the end of one year. The sum is
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Let the sum be P.
As, the interest is compounded half-yearly,
∴ R = 2%, T = 2 half years , A = ₹ 7,803∴ A = P 
1 + R 
T 100 ⇒ 7803 = P 1 + 2 2 100 ⇒ 7803 = P 1 + 1 2 50
Correct Option: C
Let the sum be P.
As, the interest is compounded half-yearly,
∴ R = 2%, T = 2 half years , A = ₹ 7,803∴ A = P 1 + R T 100 ⇒ 7803 = P 1 + 2 2 100 ⇒ 7803 = P 1 + 1 2 50 ⇒ 7803 = P × 51 × 51 50 50 ⇒ P = 7803 × 50 × 50 = ₹ 7500 51 × 51
- A certain sum of money yields ₹ 1261 as compound interest for 3 years at 5% per annum. The sum is
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Let the principal be ₹ p.
Here , CI = ₹ 1261 , R = 5%, T = 3 years
Using the given formula ,Now, C.I. = P 
1 + R T − 1 
100 ⇒ 1261 = p 1 + 5 3 − 1 100 ⇒ 1261 = p 9261 − 1 8000 ⇒ 1261 = p 9261 − 8000 8000
Correct Option: D
Let the principal be ₹ p.
Here , CI = ₹ 1261 , R = 5%, T = 3 years
Using the given formula ,Now, C.I. = P 1 + R T − 1 100 ⇒ 1261 = p 1 + 5 3 − 1 100 ⇒ 1261 = p 9261 − 1 8000 ⇒ 1261 = p 9261 − 8000 8000 ⇒ 1261 = 1261p 8000 ⇒ p = 1261 × 8000 = ₹ 8000 1261
- In what time will ₹ 10,000 amount to ₹ 13310 at 20% per annum compounded half yearly?
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Here , A = ₹ 13310 , P = ₹ 10,000
The rate of interest is compounded half yearly,
∴ r = 10% per half yearLet time = T years = T half years 2
According to the question,Amount = P 1 + R t 100 ⇒ 13310 = 10000 1 + 10 T 100 ⇒ 13310 = 11 T 10000 10
Correct Option: A
Here , A = ₹ 13310 , P = ₹ 10,000
The rate of interest is compounded half yearly,
∴ r = 10% per half yearLet time = T years = T half years 2
According to the question,Amount = P 1 + R t 100 ⇒ 13310 = 10000 1 + 10 T 100 ⇒ 13310 = 11 T 10000 10 ⇒ 11 T = 1331 = 11 3 10 1000 10 ⇒ T = 3 half years =1 1 years 2
- The compound interest on ₹ 8,000 at 15% per annum for 2 years 4 months, compounded annually is:
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Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
Using the given formula ,Amount = P 1 + R t 100 Amount = 8000 1 + 15 7/3 100 Amount = 8000 1 + 3 2 1 + 3 20 20 × 3
Correct Option: C
Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
Using the given formula ,Amount = P 1 + R t 100 Amount = 8000 1 + 15 7/3 100 Amount = 8000 1 + 3 2 1 + 3 20 20 × 3 Amount = 8000 × 23 × 23 × 21 = ₹ 11109 20 20 20
∴ Compound Interest = Amount - Principal
∴ Compound Interest = ₹ (11109 – 8000) = ₹ 3109
- At what rate per annum will ₹ 32000 yield a compound interest of ₹ 5044 in 9 months interest being compounded quarterly ?
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Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 1 + R T − 1 100 ⇒ 5044 = 32000 1 + R 3 − 1 400
[∵ Interest is compounded quarterly]⇒ 5044 = 1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20
Correct Option: A
Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 1 + R T − 1 100 ⇒ 5044 = 32000 1 + R 3 − 1 400
[∵ Interest is compounded quarterly]⇒ 5044 = 1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20 ⇒ 1 + R = 21 ⇒ R = 21 − 1 = 1 400 20 400 20 20 ⇒ R = 400 = 20 20
