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If the difference between compound interest and simple interest on a certain amount at 7% per annum for two years is Rs. 7.35, then find the principal amount.
- a)Rs. 1500
- b)Rs. 1480
- c)Rs. 1200
- d)Rs. 620
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the difference between compound interest and simple interest on a c...
Given information:
- Rate of interest = 7% per annum
- Time period = 2 years
- Difference between compound interest and simple interest = Rs. 7.35
To find: Principal amount
Let's solve the problem step by step:
Step 1: Understand the concept of compound interest and simple interest
Compound Interest:
- Compound interest is calculated on the principal amount as well as the interest earned in previous periods.
- It is given by the formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years.
Simple Interest:
- Simple interest is calculated only on the principal amount.
- It is given by the formula: A = P(1 + rt), where A is the final amount, P is the principal amount, r is the rate of interest, and t is the time period in years.
Step 2: Set up the equation using the given information
Let the principal amount be 'P'.
Compound Interest = P(1 + r/100)^t - P
Simple Interest = P * r * t / 100
According to the given information, Compound Interest - Simple Interest = Rs. 7.35
P(1 + r/100)^t - P - P * r * t / 100 = 7.35
Step 3: Substitute the values and solve the equation
Substituting the given values, we have:
P(1 + 7/100)^2 - P - P * 7 * 2 / 100 = 7.35
P(1 + 0.07)^2 - P - 0.14P = 7.35
P(1.07)^2 - P - 0.14P = 7.35
1.1449P - P - 0.14P = 7.35
0.0049P = 7.35
P = 7.35 / 0.0049
P ≈ Rs. 1500
Therefore, the principal amount is approximately Rs. 1500, which corresponds to option A.
- Rate of interest = 7% per annum
- Time period = 2 years
- Difference between compound interest and simple interest = Rs. 7.35
To find: Principal amount
Let's solve the problem step by step:
Step 1: Understand the concept of compound interest and simple interest
Compound Interest:
- Compound interest is calculated on the principal amount as well as the interest earned in previous periods.
- It is given by the formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time period in years.
Simple Interest:
- Simple interest is calculated only on the principal amount.
- It is given by the formula: A = P(1 + rt), where A is the final amount, P is the principal amount, r is the rate of interest, and t is the time period in years.
Step 2: Set up the equation using the given information
Let the principal amount be 'P'.
Compound Interest = P(1 + r/100)^t - P
Simple Interest = P * r * t / 100
According to the given information, Compound Interest - Simple Interest = Rs. 7.35
P(1 + r/100)^t - P - P * r * t / 100 = 7.35
Step 3: Substitute the values and solve the equation
Substituting the given values, we have:
P(1 + 7/100)^2 - P - P * 7 * 2 / 100 = 7.35
P(1 + 0.07)^2 - P - 0.14P = 7.35
P(1.07)^2 - P - 0.14P = 7.35
1.1449P - P - 0.14P = 7.35
0.0049P = 7.35
P = 7.35 / 0.0049
P ≈ Rs. 1500
Therefore, the principal amount is approximately Rs. 1500, which corresponds to option A.
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If the difference between compound interest and simple interest on a certain amount at 7% per annum for two years is Rs. 7.35, then find the principal amount.a)Rs. 1500b)Rs. 1480c)Rs. 1200d)Rs. 620Correct answer is option 'A'. Can you explain this answer?
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