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If the difference between compound interest and simple interest on a certain amount for two years is Rs. 7.35 and the rate of interest is 7%, then find the principal.
- a)Rs. 1500
- b)Rs. 1400
- c)Rs. 1200
- d)Rs. 1300
- e)None of these
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:
Difference between compound interest and simple interest for 2 years = Rs. 7.35
Rate of interest = 7%
To find:
Principal amount
Let's solve this step by step.
Step 1: Calculate the difference between compound interest and simple interest for 1 year.
Since the question asks for the difference for 2 years, we need to find the difference for 1 year first.
Using the formula for compound interest:
Compound Interest = P(1 + r/100)^n - P
Where,
P = Principal amount
r = Rate of interest
n = Time period
For 1 year:
Compound Interest = P(1 + r/100)^1 - P
Simple Interest = (P * r * 1)/100
Given:
Compound Interest - Simple Interest = Rs. 7.35
Therefore,
P(1 + 7/100)^1 - P - (P * 7 * 1)/100 = 7.35
Simplifying the equation:
P(1.07) - P(0.07) = 7.35
0.07P = 7.35
P = 7.35/0.07
Step 2: Calculate the principal amount for 2 years.
Now that we have the principal amount for 1 year, we can find the principal amount for 2 years using the same formula.
For 2 years:
Compound Interest = P(1 + r/100)^2 - P
Simple Interest = (P * r * 2)/100
Given:
Compound Interest - Simple Interest = Rs. 7.35
Therefore,
P(1 + 7/100)^2 - P - (P * 7 * 2)/100 = 7.35
Simplifying the equation:
P(1.07)^2 - 2P(0.07) = 7.35
P(1.07)(1.07) - 2P(0.07) = 7.35
1.1449P - 0.14P = 7.35
1.0049P = 7.35
P = 7.35/1.0049
Calculating the value of P:
P = Rs. 1500
Therefore, the principal amount is Rs. 1500.
Hence, option A - Rs. 1500 is the correct answer.
Difference between compound interest and simple interest for 2 years = Rs. 7.35
Rate of interest = 7%
To find:
Principal amount
Let's solve this step by step.
Step 1: Calculate the difference between compound interest and simple interest for 1 year.
Since the question asks for the difference for 2 years, we need to find the difference for 1 year first.
Using the formula for compound interest:
Compound Interest = P(1 + r/100)^n - P
Where,
P = Principal amount
r = Rate of interest
n = Time period
For 1 year:
Compound Interest = P(1 + r/100)^1 - P
Simple Interest = (P * r * 1)/100
Given:
Compound Interest - Simple Interest = Rs. 7.35
Therefore,
P(1 + 7/100)^1 - P - (P * 7 * 1)/100 = 7.35
Simplifying the equation:
P(1.07) - P(0.07) = 7.35
0.07P = 7.35
P = 7.35/0.07
Step 2: Calculate the principal amount for 2 years.
Now that we have the principal amount for 1 year, we can find the principal amount for 2 years using the same formula.
For 2 years:
Compound Interest = P(1 + r/100)^2 - P
Simple Interest = (P * r * 2)/100
Given:
Compound Interest - Simple Interest = Rs. 7.35
Therefore,
P(1 + 7/100)^2 - P - (P * 7 * 2)/100 = 7.35
Simplifying the equation:
P(1.07)^2 - 2P(0.07) = 7.35
P(1.07)(1.07) - 2P(0.07) = 7.35
1.1449P - 0.14P = 7.35
1.0049P = 7.35
P = 7.35/1.0049
Calculating the value of P:
P = Rs. 1500
Therefore, the principal amount is Rs. 1500.
Hence, option A - Rs. 1500 is the correct answer.
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If the difference between compound interest and simple interest on a certain amount for two years is Rs. 7.35 and the rate of interest is 7%, then find the principal.a)Rs. 1500b)Rs. 1400c)Rs. 1200d)Rs. 1300e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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