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The difference between the compound and simple interest on a certain sum for 2 years at the rate of 8% per annum is Rs.80,What is the sum?
- a)11,880
- b)12,500
- c)13,250
- d)14,270
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The difference between the compound and simple interest on a certain s...
Difference in simple and compound interest at the end of 2 years occurs because there is interest on first year interest. So Difference = P×(R100)2P×(R100)2
⇒ 80 = P×(8100)2P×(8100)2
⇒ P=80×(1008)2P=80×(1008)2 = 12,500
⇒ 80 = P×(8100)2P×(8100)2
⇒ P=80×(1008)2P=80×(1008)2 = 12,500
Most Upvoted Answer
The difference between the compound and simple interest on a certain s...
Given:
- Rate of interest = 8%
- Time period = 2 years
- Difference between compound and simple interest = Rs. 80
To find:
The sum of money (principal)
Assumption:
Let's assume the principal as P.
Formula:
The formula for calculating the compound interest is:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
- P is the principal amount
- r is the rate of interest (in decimal form)
- n is the number of times that interest is compounded per time period
- t is the time period (in years)
The formula for calculating the simple interest is:
Simple Interest = P * r * t
Calculation:
1. Difference between compound and simple interest = Compound Interest - Simple Interest
Rs. 80 = P(1 + 0.08/1)^(1*2) - P * 0.08 * 2
2. Simplifying the equation:
Rs. 80 = P(1.08)^2 - P * 0.16
3. Expanding the equation:
Rs. 80 = 1.1664P - 0.16P
4. Combining like terms:
Rs. 80 = 1.0064P
5. Dividing both sides by 1.0064:
P = Rs. 80 / 1.0064
6. Calculating the value of P:
P ≈ Rs. 79.37
Therefore, the sum of money (principal) is approximately Rs. 79.37. However, none of the given options match this value. Hence, there may be an error in the given options or in the calculations.
- Rate of interest = 8%
- Time period = 2 years
- Difference between compound and simple interest = Rs. 80
To find:
The sum of money (principal)
Assumption:
Let's assume the principal as P.
Formula:
The formula for calculating the compound interest is:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
- P is the principal amount
- r is the rate of interest (in decimal form)
- n is the number of times that interest is compounded per time period
- t is the time period (in years)
The formula for calculating the simple interest is:
Simple Interest = P * r * t
Calculation:
1. Difference between compound and simple interest = Compound Interest - Simple Interest
Rs. 80 = P(1 + 0.08/1)^(1*2) - P * 0.08 * 2
2. Simplifying the equation:
Rs. 80 = P(1.08)^2 - P * 0.16
3. Expanding the equation:
Rs. 80 = 1.1664P - 0.16P
4. Combining like terms:
Rs. 80 = 1.0064P
5. Dividing both sides by 1.0064:
P = Rs. 80 / 1.0064
6. Calculating the value of P:
P ≈ Rs. 79.37
Therefore, the sum of money (principal) is approximately Rs. 79.37. However, none of the given options match this value. Hence, there may be an error in the given options or in the calculations.
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The difference between the compound and simple interest on a certain sum for 2 years at the rate of 8% per annum is Rs.80,What is the sum?a)11,880b)12,500c)13,250d)14,270Correct answer is option 'B'. Can you explain this answer?
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