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What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
- a)Rs. 2.04
- b)Rs. 3.06
- c)Rs. 4.80
- d)Rs. 8.30
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
What is the difference between the compound interests on Rs. 5000 for ...
C.I. when interest compounded yearly
= Rs. [ 5000 x (1 + 4/100) x {1 + (1/2 x 4)/ 100}]
= Rs. 5000 x 26/25 x 51/50
= Rs. 5304.
and, C.I. when interest is compounded half-yearly
= Rs.5000 x (1 + 2 /100) ^3.
= Rs. 5000 x 51/50 x 51/50 x 51/50.
= Rs. 5306.04
The required Difference = Rs. (5306.04 - 5304) = Rs. 2.04.
= Rs. [ 5000 x (1 + 4/100) x {1 + (1/2 x 4)/ 100}]
= Rs. 5000 x 26/25 x 51/50
= Rs. 5304.
and, C.I. when interest is compounded half-yearly
= Rs.5000 x (1 + 2 /100) ^3.
= Rs. 5000 x 51/50 x 51/50 x 51/50.
= Rs. 5306.04
The required Difference = Rs. (5306.04 - 5304) = Rs. 2.04.
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Community Answer
What is the difference between the compound interests on Rs. 5000 for ...
Calculation of Compound Interest:
Compound Interest formula: A = P(1 + r/n)^(nt)
Where,
A = Total amount after n years
P = Principal amount (Rs. 5000 in this case)
r = Annual interest rate (4%)
n = Number of times interest is compounded per year
t = Number of years (1 year in this case)
When interest is compounded yearly:
A = 5000(1 + 0.04/1)^(1*1)
A = 5000(1.04)
A = Rs. 5200
Compound Interest = Total amount - Principal amount
Compound Interest = Rs. 5200 - Rs. 5000
Compound Interest = Rs. 200
When interest is compounded half-yearly:
n = 2 (compounded half-yearly)
r = 4% per annum
A = 5000(1 + 0.04/2)^(2*1)
A = 5000(1 + 0.02)^2
A = 5000(1.02)^2
A = 5000(1.0404)
A = Rs. 5202
Compound Interest = Total amount - Principal amount
Compound Interest = Rs. 5202 - Rs. 5000
Compound Interest = Rs. 202
Difference in Compound Interests:
The difference between compound interests when interest is compounded yearly and half-yearly:
Rs. 202 - Rs. 200 = Rs. 2.04
Therefore, the correct answer is option A) Rs. 2.04.
Compound Interest formula: A = P(1 + r/n)^(nt)
Where,
A = Total amount after n years
P = Principal amount (Rs. 5000 in this case)
r = Annual interest rate (4%)
n = Number of times interest is compounded per year
t = Number of years (1 year in this case)
When interest is compounded yearly:
A = 5000(1 + 0.04/1)^(1*1)
A = 5000(1.04)
A = Rs. 5200
Compound Interest = Total amount - Principal amount
Compound Interest = Rs. 5200 - Rs. 5000
Compound Interest = Rs. 200
When interest is compounded half-yearly:
n = 2 (compounded half-yearly)
r = 4% per annum
A = 5000(1 + 0.04/2)^(2*1)
A = 5000(1 + 0.02)^2
A = 5000(1.02)^2
A = 5000(1.0404)
A = Rs. 5202
Compound Interest = Total amount - Principal amount
Compound Interest = Rs. 5202 - Rs. 5000
Compound Interest = Rs. 202
Difference in Compound Interests:
The difference between compound interests when interest is compounded yearly and half-yearly:
Rs. 202 - Rs. 200 = Rs. 2.04
Therefore, the correct answer is option A) Rs. 2.04.
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What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?a)Rs. 2.04b)Rs. 3.06c)Rs. 4.80d)Rs. 8.30Correct answer is option 'A'. Can you explain this answer?
Question Description
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