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The difference between simple interest and compound interest for 2 years on the sum Rs. 2900 at a certain rate is Rs. 14.21. What is annual rate of interest?
- a)9%
- b)5%
- c)7%
- d)8%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The difference between simple interest and compound interest for 2 yea...
We know that the difference between the simple interest (SI2) & compound interest (CI2) for 2 years [compounded annually] on a sum of Rs. P at a rate R is,
Now the given information, P = Rs. 2900, CI2 – SI2 = Rs. 14.21
Putting the values we get,
The annual rate of interest is 7%
Now the given information, P = Rs. 2900, CI2 – SI2 = Rs. 14.21
Putting the values we get,
The annual rate of interest is 7%
Most Upvoted Answer
The difference between simple interest and compound interest for 2 yea...
Given:
Principal amount (P) = Rs. 2900
Time (t) = 2 years
Difference between compound interest and simple interest (S) = Rs. 14.21
To find:
Annual rate of interest (R)
Explanation:
The formula for simple interest is:
Simple Interest (SI) = (P * R * t) / 100
The formula for compound interest is:
Compound Interest (CI) = P * (1 + R/100)^t - P
Given that the difference between compound interest and simple interest is Rs. 14.21, we can write it as:
CI - SI = 14.21
Substituting the formulas for CI and SI, we have:
P * (1 + R/100)^t - P - (P * R * t) / 100 = 14.21
Simplifying the equation, we get:
[(1 + R/100)^t - 1 - (R * t)/100] * P = 14.21
Now, substituting the given values, we have:
[(1 + R/100)^2 - 1 - 2R/100] * 2900 = 14.21
Expanding and simplifying the equation further, we get:
[(100 + R)^2 - 10000 - 200R] * 29 = 1421
Now, let's solve this equation to find the value of R.
Solution:
[(100 + R)^2 - 10000 - 200R] * 29 = 1421
Expanding the equation:
(10000 + 200R + R^2 - 10000 - 200R) * 29 = 1421
Simplifying the equation:
R^2 * 29 = 1421
Dividing by 29:
R^2 = 49
Taking the square root:
R = 7 or -7
Since the rate of interest cannot be negative, the annual rate of interest is 7%.
Hence, the correct answer is option C) 7%.
Principal amount (P) = Rs. 2900
Time (t) = 2 years
Difference between compound interest and simple interest (S) = Rs. 14.21
To find:
Annual rate of interest (R)
Explanation:
The formula for simple interest is:
Simple Interest (SI) = (P * R * t) / 100
The formula for compound interest is:
Compound Interest (CI) = P * (1 + R/100)^t - P
Given that the difference between compound interest and simple interest is Rs. 14.21, we can write it as:
CI - SI = 14.21
Substituting the formulas for CI and SI, we have:
P * (1 + R/100)^t - P - (P * R * t) / 100 = 14.21
Simplifying the equation, we get:
[(1 + R/100)^t - 1 - (R * t)/100] * P = 14.21
Now, substituting the given values, we have:
[(1 + R/100)^2 - 1 - 2R/100] * 2900 = 14.21
Expanding and simplifying the equation further, we get:
[(100 + R)^2 - 10000 - 200R] * 29 = 1421
Now, let's solve this equation to find the value of R.
Solution:
[(100 + R)^2 - 10000 - 200R] * 29 = 1421
Expanding the equation:
(10000 + 200R + R^2 - 10000 - 200R) * 29 = 1421
Simplifying the equation:
R^2 * 29 = 1421
Dividing by 29:
R^2 = 49
Taking the square root:
R = 7 or -7
Since the rate of interest cannot be negative, the annual rate of interest is 7%.
Hence, the correct answer is option C) 7%.
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The difference between simple interest and compound interest for 2 years on the sum Rs. 2900 at a certain rate is Rs. 14.21. What is annual rate of interest?a)9%b)5%c)7%d)8%Correct answer is option 'C'. Can you explain this answer?
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