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The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 450. What is definitely the rate of interest per cent per annum?
- a)8400
- b)4800
- c)7800
- d)Data inadequate
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The difference between the total simple interest and the total compoun...
Difference = Pr /(100)2
= (450×100×100)/(P×r2)
P is not given
= (450×100×100)/(P×r2)
P is not given
Most Upvoted Answer
The difference between the total simple interest and the total compoun...
The problem:
The problem states that the difference between the total simple interest and the total compound interest compounded annually on a sum of money at the end of two years is Rs. 450. We need to find the rate of interest per cent per annum.
Let's assume:
Let's assume the principal amount is P and the rate of interest is R%.
Calculating Simple Interest:
The formula to calculate simple interest is:
Simple Interest (SI) = (P * R * T) / 100
Calculating Compound Interest:
The formula to calculate compound interest is:
Compound Interest (CI) = P * (1 + R/100)^T - P
Calculating the difference:
Given that the difference between the total simple interest and the total compound interest after two years is Rs. 450, we can write the equation as:
SI - CI = 450
Substituting the formulas:
Substituting the formulas for SI and CI, we get:
(P * R * 2) / 100 - P * (1 + R/100)^2 + P = 450
Simplifying the equation:
Simplifying the equation further, we have:
2PR/100 - P(1 + R/100)^2 + P = 450
Expanding the equation:
Expanding the equation, we get:
2PR/100 - P(1 + 2R/100 + R^2/10000) + P = 450
Cancelling out terms:
Cancelling out the common terms, we have:
2PR/100 - 2PR/100 - PR^2/10000 + P = 450
Simplifying the equation:
Simplifying the equation further, we get:
PR^2/10000 = 450
Re-arranging the equation:
Re-arranging the equation, we have:
R^2 = (450 * 10000) / P
Calculating the rate of interest:
To find the rate of interest, we need to take the square root of both sides of the equation:
R = sqrt((450 * 10000) / P)
Conclusion:
Since the principal amount (P) is not given, we cannot determine the exact rate of interest. Therefore, the data is inadequate to find the rate of interest per cent per annum. Hence, option 'D' is the correct answer.
The problem states that the difference between the total simple interest and the total compound interest compounded annually on a sum of money at the end of two years is Rs. 450. We need to find the rate of interest per cent per annum.
Let's assume:
Let's assume the principal amount is P and the rate of interest is R%.
Calculating Simple Interest:
The formula to calculate simple interest is:
Simple Interest (SI) = (P * R * T) / 100
Calculating Compound Interest:
The formula to calculate compound interest is:
Compound Interest (CI) = P * (1 + R/100)^T - P
Calculating the difference:
Given that the difference between the total simple interest and the total compound interest after two years is Rs. 450, we can write the equation as:
SI - CI = 450
Substituting the formulas:
Substituting the formulas for SI and CI, we get:
(P * R * 2) / 100 - P * (1 + R/100)^2 + P = 450
Simplifying the equation:
Simplifying the equation further, we have:
2PR/100 - P(1 + R/100)^2 + P = 450
Expanding the equation:
Expanding the equation, we get:
2PR/100 - P(1 + 2R/100 + R^2/10000) + P = 450
Cancelling out terms:
Cancelling out the common terms, we have:
2PR/100 - 2PR/100 - PR^2/10000 + P = 450
Simplifying the equation:
Simplifying the equation further, we get:
PR^2/10000 = 450
Re-arranging the equation:
Re-arranging the equation, we have:
R^2 = (450 * 10000) / P
Calculating the rate of interest:
To find the rate of interest, we need to take the square root of both sides of the equation:
R = sqrt((450 * 10000) / P)
Conclusion:
Since the principal amount (P) is not given, we cannot determine the exact rate of interest. Therefore, the data is inadequate to find the rate of interest per cent per annum. Hence, option 'D' is the correct answer.
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Community Answer
The difference between the total simple interest and the total compoun...
Difference = Pr /(100)2
= (450×100×100)/(P×r2)
P is not given
= (450×100×100)/(P×r2)
P is not given
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