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Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.
- a)Rs. 2000
- b)Rs. 2200
- c)Rs. 1000
- d)Rs. 1100
Correct answer is option 'A'. Can you explain this answer?
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Find the principal if the interest compounded at the rate of 10% per ...
P = ?, Cl = Rs. 420, R = 10%, T = 2 years.
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Find the principal if the interest compounded at the rate of 10% per ...
Given:
- Rate of interest = 10% per annum
- Time period = 2 years
- Compound interest = Rs. 420
To find:
- Principal amount
Solution:
Step 1: Understanding the formula for compound interest:
The formula to calculate compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest (in decimal form)
n = Number of times interest is compounded per year
t = Time in years
Step 2: Given values:
Rate of interest (r) = 10% = 0.1 (in decimal form)
Time period (t) = 2 years
Compound interest = Rs. 420
Step 3: Substitute the given values into the formula:
A = P(1 + r/n)^(nt)
Rs. 420 = P(1 + 0.1/1)^(1*2)
Simplify the equation:
420 = P(1 + 0.1)^2
Step 4: Solve the equation to find the principal amount:
420 = P(1.1)^2
420 = P(1.21)
Divide both sides of the equation by 1.21:
420/1.21 = P
P = 347.1074
The principal amount is approximately Rs. 347.1074.
Step 5: Round off the principal amount:
Since the principal amount cannot be in decimal form, we round off the value to the nearest whole number.
So, the rounded off principal amount is Rs. 347.
However, none of the given options match with the calculated principal amount. Therefore, there might be an error in the options provided or in the calculation.
Correct Answer:
Since the calculated principal amount does not match with any of the given options, it is not possible to determine the correct answer based on the information provided.
- Rate of interest = 10% per annum
- Time period = 2 years
- Compound interest = Rs. 420
To find:
- Principal amount
Solution:
Step 1: Understanding the formula for compound interest:
The formula to calculate compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Rate of interest (in decimal form)
n = Number of times interest is compounded per year
t = Time in years
Step 2: Given values:
Rate of interest (r) = 10% = 0.1 (in decimal form)
Time period (t) = 2 years
Compound interest = Rs. 420
Step 3: Substitute the given values into the formula:
A = P(1 + r/n)^(nt)
Rs. 420 = P(1 + 0.1/1)^(1*2)
Simplify the equation:
420 = P(1 + 0.1)^2
Step 4: Solve the equation to find the principal amount:
420 = P(1.1)^2
420 = P(1.21)
Divide both sides of the equation by 1.21:
420/1.21 = P
P = 347.1074
The principal amount is approximately Rs. 347.1074.
Step 5: Round off the principal amount:
Since the principal amount cannot be in decimal form, we round off the value to the nearest whole number.
So, the rounded off principal amount is Rs. 347.
However, none of the given options match with the calculated principal amount. Therefore, there might be an error in the options provided or in the calculation.
Correct Answer:
Since the calculated principal amount does not match with any of the given options, it is not possible to determine the correct answer based on the information provided.
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Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.a)Rs. 2000b)Rs. 2200c)Rs. 1000d)Rs. 1100Correct answer is option 'A'. Can you explain this answer?
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