Compound Interest
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according as the interest is compounded yearly or halfyearly?What is the difference between compound interest on ₹ 5,000 for 1 1 at 4% per annum 2
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Given in question , Principal = ₹ 5000 , Time = 1.5 years , Rate = 5%
When Interest is compounded yearly ,Compound Interest = 5000 
1 + 4 
1.5 − 5000 100 Compound Interest = 5000 26 1.5 − 5000 25
Compound Interest = 5302.9805 – 5000 = ₹ 302.9805
Again , when compounded half yearly ,C.I. = 5000 1 + 2 3 − 5000 100
Correct Option: B
Given in question , Principal = ₹ 5000 , Time = 1.5 years , Rate = 5%
When Interest is compounded yearly ,Compound Interest = 5000 1 + 4 1.5 − 5000 100 Compound Interest = 5000 26 1.5 − 5000 25
Compound Interest = 5302.9805 – 5000 = ₹ 302.9805
Again , when compounded half yearly ,C.I. = 5000 1 + 2 3 − 5000 100
C.I. = 5306.04 – 5000 = ₹ 306.04
∴ Required difference = ₹ (306.04 – 302.9805) = ₹ 3.059 = ₹ 3.06
- If the difference between the compound interest, compounded every six months, and the simple interest on a certain sum of money at the rate of 12% per annum for one year is ₹ 36, the sum is :
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As the interest was compounded half-yearly,
we changed r to r and t to 2t. 2
∴ T = 1 year & R = 6%
Correct Option: A
As the interest was compounded half-yearly,
we changed r to r and t to 2t. 2
∴ T = 1 year & R = 6%Sum = 36 × 100 × 100 = ₹ 10000 6 × 6
- There is 40% increase in an amount in 8 years at simple interest. What will be the compound interest (in rupees) of Rs 30000 after 2 years at the same rate ?
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According to the question,
If principal = Rs. 100 then interest = Rs. 40.∴ Rate = S.I. × 100 Principal × Time Rate = 40 × 100 = 5% per annum 100 × 8
Case II.∴ A = P 1 + R T 100 A = 30000 1 + 5 2 100 A = 30000 1 + 1 2 20
Correct Option: D
According to the question,
If principal = Rs. 100 then interest = Rs. 40.∴ Rate = S.I. × 100 Principal × Time Rate = 40 × 100 = 5% per annum 100 × 8
Case II.∴ A = P 1 + R T 100 A = 30000 1 + 5 2 100 A = 30000 1 + 1 2 20 A = 30000 20 + 1 2 20 A = 30000 × 21 × 21 = Rs. 33075 20 20
∴ C. I. = Amount - Principal
∴ C. I. = Rs. (33075 – 30000) = Rs. 3075
- If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is :
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Given , Simple Interest S.I. = Rs. 50 , Time = 2 years , Rate = 5%
Using the given formula ,Principal = S.I. × 100 Time × Rate Principal = 50 × 100 = Rs. 500 2 × 5 ∴ C.I. = P 
1 + R T − 1 
100 C.I. = 500 1 + 5 2 − 1 100 C.I. = 500 1 + 1 2 − 1 20 C.I. = 500 21 2 − 1 20
Correct Option: B
Given , Simple Interest S.I. = Rs. 50 , Time = 2 years , Rate = 5%
Using the given formula ,Principal = S.I. × 100 Time × Rate Principal = 50 × 100 = Rs. 500 2 × 5 ∴ C.I. = P 1 + R T − 1 100 C.I. = 500 1 + 5 2 − 1 100 C.I. = 500 1 + 1 2 − 1 20 C.I. = 500 21 2 − 1 20 C.I. = 500 441 − 1 400 C.I. = 500 × 41 = Rs. 51.25 400
- The difference between compound interest and simple interest of a sum for 2 years at 8 percent is ₹ 768. The sum is
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Here , Difference = C.I. - S.I. = ₹ 768 , Time = 2 years , Rate = 8%
Using the given formula ,Sum = (CI – SI) 100 2 r
Correct Option: C
Here , Difference = C.I. - S.I. = ₹ 768 , Time = 2 years , Rate = 8%
Using the given formula ,Sum = (CI – SI) 100 2 r Sum = 768 × 100 2 = ₹ 1,20,000 8
