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The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.
(a) Re. 1/-
(b) Rs. 28/-
(c) Rs. 35/-
(d) Rs. 40/-?
(a) Re. 1/-
(b) Rs. 28/-
(c) Rs. 35/-
(d) Rs. 40/-?
Most Upvoted Answer
The difference between compound interest, compounded semi annually and...
Understanding Simple Interest
Simple interest is calculated using the formula:
- Simple Interest (SI) = Principal × Rate × Time
For Rs. 400 at 10% p.a. for one year:
- SI = 400 × 10/100 × 1 = Rs. 40
Calculating Compound Interest (Compounded Semi-Annually)
Compound interest is calculated using the formula:
- Compound Interest (CI) = Principal × (1 + Rate/n)^(nt) - Principal
Where:
- n = number of times interest is compounded per year (2 for semi-annual)
- t = time in years (1 year)
So, for Rs. 400 at 10% p.a. compounded semi-annually:
- CI = 400 × (1 + 0.10/2)^(2*1) - 400
- CI = 400 × (1 + 0.05)^2 - 400
- CI = 400 × (1.1025) - 400
- CI = 440.99 - 400 = Rs. 40.99 (approximately)
Finding the Difference
Now, we calculate the difference between compound interest and simple interest:
- Difference = CI - SI
- Difference = 40.99 - 40 = Rs. 0.99
Conclusion
Given the options:
- (a) Re. 1/-
- (b) Rs. 28/-
- (c) Rs. 35/-
- (d) Rs. 40/-
The closest answer to the difference of Rs. 0.99 is (a) Re. 1/-.
This illustrates how the difference between compound and simple interest can vary based on the compounding frequency and principal amount.
Simple interest is calculated using the formula:
- Simple Interest (SI) = Principal × Rate × Time
For Rs. 400 at 10% p.a. for one year:
- SI = 400 × 10/100 × 1 = Rs. 40
Calculating Compound Interest (Compounded Semi-Annually)
Compound interest is calculated using the formula:
- Compound Interest (CI) = Principal × (1 + Rate/n)^(nt) - Principal
Where:
- n = number of times interest is compounded per year (2 for semi-annual)
- t = time in years (1 year)
So, for Rs. 400 at 10% p.a. compounded semi-annually:
- CI = 400 × (1 + 0.10/2)^(2*1) - 400
- CI = 400 × (1 + 0.05)^2 - 400
- CI = 400 × (1.1025) - 400
- CI = 440.99 - 400 = Rs. 40.99 (approximately)
Finding the Difference
Now, we calculate the difference between compound interest and simple interest:
- Difference = CI - SI
- Difference = 40.99 - 40 = Rs. 0.99
Conclusion
Given the options:
- (a) Re. 1/-
- (b) Rs. 28/-
- (c) Rs. 35/-
- (d) Rs. 40/-
The closest answer to the difference of Rs. 0.99 is (a) Re. 1/-.
This illustrates how the difference between compound and simple interest can vary based on the compounding frequency and principal amount.
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The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-?.
The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between compound interest, compounded semi annually and simple interest on Rs. 400/- at 10% p.a. for one year.(a) Re. 1/-(b) Rs. 28/-(c) Rs. 35/-(d) Rs. 40/-?.
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