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What is the difference (in Rs) between the compound interests on Rs. 1000 for 1 year at 10% per annum compounded yearly and half-yearly?
- a)1.5
- b)0.5
- c)2.5
- d)3.5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
What is the difference (in Rs) between the compound interests on Rs. 1...
GIVEN:
P = Rs. 1000
Rate = 10%
Time = 1 year
FORMULA USED:
On a sum of Rs. P at rate of R% per annum after n years,
Compound interest = P[(1 + R/100)n – 1], when compounded annually
Compound interest = P[(1 + R/200)2n – 1], when compounded half-yearly
CALCULATION:
Interest compounded annually = 1000 × (1 + 10/100 – 1) = 1000 × 0.1 = Rs. 100
Interest compounded half-yearly = 1000 × [(1 + 10/200)2 – 1] = 1000 × 0.1025 = Rs. 102.5
∴ Required difference = 102.5 – 100 = Rs. 2.5
Most Upvoted Answer
What is the difference (in Rs) between the compound interests on Rs. 1...
Calculation of Compound Interest:
To find the compound interest for Rs. 1000 at 10% per annum compounded yearly and half-yearly, we can use the formula:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
- P = principal amount (Rs. 1000)
- r = annual interest rate (10% or 0.10)
- n = number of times interest is compounded per year (1 for yearly, 2 for half-yearly)
- t = time in years (1 year)
Compound Interest with Yearly Compounding:
Putting the values in the formula:
Compound Interest = 1000(1 + 0.10/1)^(1*1) - 1000
Compound Interest = 1000(1 + 0.10) - 1000
Compound Interest = 1000(1.10) - 1000
Compound Interest = 1100 - 1000
Compound Interest = Rs. 100
Compound Interest with Half-Yearly Compounding:
Putting the values in the formula:
Compound Interest = 1000(1 + 0.10/2)^(2*1) - 1000
Compound Interest = 1000(1 + 0.05)^(2) - 1000
Compound Interest = 1000(1.05)^2 - 1000
Compound Interest = 1000(1.1025) - 1000
Compound Interest = 1102.50 - 1000
Compound Interest = Rs. 102.50
Difference in Compound Interests:
The difference in compound interests between yearly and half-yearly compounding:
= Rs. 102.50 - Rs. 100
= Rs. 2.50
Therefore, the difference in compound interests on Rs. 1000 for 1 year at 10% per annum compounded yearly and half-yearly is Rs. 2.50. Hence, option C (2.5) is the correct answer.
To find the compound interest for Rs. 1000 at 10% per annum compounded yearly and half-yearly, we can use the formula:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
- P = principal amount (Rs. 1000)
- r = annual interest rate (10% or 0.10)
- n = number of times interest is compounded per year (1 for yearly, 2 for half-yearly)
- t = time in years (1 year)
Compound Interest with Yearly Compounding:
Putting the values in the formula:
Compound Interest = 1000(1 + 0.10/1)^(1*1) - 1000
Compound Interest = 1000(1 + 0.10) - 1000
Compound Interest = 1000(1.10) - 1000
Compound Interest = 1100 - 1000
Compound Interest = Rs. 100
Compound Interest with Half-Yearly Compounding:
Putting the values in the formula:
Compound Interest = 1000(1 + 0.10/2)^(2*1) - 1000
Compound Interest = 1000(1 + 0.05)^(2) - 1000
Compound Interest = 1000(1.05)^2 - 1000
Compound Interest = 1000(1.1025) - 1000
Compound Interest = 1102.50 - 1000
Compound Interest = Rs. 102.50
Difference in Compound Interests:
The difference in compound interests between yearly and half-yearly compounding:
= Rs. 102.50 - Rs. 100
= Rs. 2.50
Therefore, the difference in compound interests on Rs. 1000 for 1 year at 10% per annum compounded yearly and half-yearly is Rs. 2.50. Hence, option C (2.5) is the correct answer.
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What is the difference (in Rs) between the compound interests on Rs. 1000 for 1 year at 10% per annum compounded yearly and half-yearly?a)1.5b)0.5c)2.5d)3.5Correct answer is option 'C'. Can you explain this answer?
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