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A sum of Rs. 18000 is deposited in a bank for two years which gives 20% rate of interest per annum compounded annually. If the given interest compounded half-yearly, then interest would have been how many percent more than its present interest.
- a)9.45%
- b)11.23%
- c)5.4%
- d)12.03%
Correct answer is option 'C'. Can you explain this answer?
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A sum of Rs. 18000 is deposited in a bank for two years which gives 2...
(Percentage of compound interest at annually = 44 %
Percentage of compound interest at half-yearly = 46.41%
Required % =2.41/44×100=5.4%)
Most Upvoted Answer
A sum of Rs. 18000 is deposited in a bank for two years which gives 2...
Solution:
Given:
Principal amount (P) = Rs. 18000
Rate of interest (R) = 20%
Time (T) = 2 years
To find:
The difference in interest when compounded half-yearly compared to compounded annually.
Formula for compound interest:
Compound Interest (CI) = P(1 + R/100)^n - P
Where,
CI is the compound interest,
P is the principal amount,
R is the rate of interest,
n is the number of times the interest is compounded in a year.
Case 1: Interest compounded annually
In this case, the interest is compounded once in a year.
Using the formula, the amount after 2 years can be calculated as:
A = P(1 + R/100)^n
= 18000(1 + 20/100)^2
= 18000(1 + 0.2)^2
= 18000(1.2)^2
= 18000 * 1.44
= 25920
The compound interest for 2 years compounded annually is:
CI = A - P
= 25920 - 18000
= 7920
Case 2: Interest compounded half-yearly
In this case, the interest is compounded twice in a year.
Using the formula, the amount after 2 years can be calculated as:
A = P(1 + R/100)^n
= 18000(1 + 20/200)^2*2
= 18000(1 + 0.1)^4
= 18000(1.1)^4
= 18000 * 1.4641
= 26434.8
The compound interest for 2 years compounded half-yearly is:
CI = A - P
= 26434.8 - 18000
= 8434.8
The difference in interest is given by:
Difference = CI(compounded half-yearly) - CI(compounded annually)
= 8434.8 - 7920
= 514.8
The percentage difference can be calculated as:
Percentage difference = (Difference / CI(compounded annually)) * 100
= (514.8 / 7920) * 100
≈ 6.5%
Therefore, the interest compounded half-yearly is approximately 6.5% more than the interest compounded annually.
Conclusion:
The interest compounded half-yearly is approximately 6.5% more than the interest compounded annually.
Given:
Principal amount (P) = Rs. 18000
Rate of interest (R) = 20%
Time (T) = 2 years
To find:
The difference in interest when compounded half-yearly compared to compounded annually.
Formula for compound interest:
Compound Interest (CI) = P(1 + R/100)^n - P
Where,
CI is the compound interest,
P is the principal amount,
R is the rate of interest,
n is the number of times the interest is compounded in a year.
Case 1: Interest compounded annually
In this case, the interest is compounded once in a year.
Using the formula, the amount after 2 years can be calculated as:
A = P(1 + R/100)^n
= 18000(1 + 20/100)^2
= 18000(1 + 0.2)^2
= 18000(1.2)^2
= 18000 * 1.44
= 25920
The compound interest for 2 years compounded annually is:
CI = A - P
= 25920 - 18000
= 7920
Case 2: Interest compounded half-yearly
In this case, the interest is compounded twice in a year.
Using the formula, the amount after 2 years can be calculated as:
A = P(1 + R/100)^n
= 18000(1 + 20/200)^2*2
= 18000(1 + 0.1)^4
= 18000(1.1)^4
= 18000 * 1.4641
= 26434.8
The compound interest for 2 years compounded half-yearly is:
CI = A - P
= 26434.8 - 18000
= 8434.8
The difference in interest is given by:
Difference = CI(compounded half-yearly) - CI(compounded annually)
= 8434.8 - 7920
= 514.8
The percentage difference can be calculated as:
Percentage difference = (Difference / CI(compounded annually)) * 100
= (514.8 / 7920) * 100
≈ 6.5%
Therefore, the interest compounded half-yearly is approximately 6.5% more than the interest compounded annually.
Conclusion:
The interest compounded half-yearly is approximately 6.5% more than the interest compounded annually.
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