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Compound interest on a certain sum for 2 years at 12(1/2)% per annum is Rs 170. Find the sum.
- a)345
- b)740
- c)640
- d)525
Correct answer is option 'C'. Can you explain this answer?
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Compound interest on a certain sum for 2 years at 12(1/2)% per annum i...
To find the sum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal sum (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we are given:
r = 12(1/2)% per annum = 12.5% = 0.125 (as a decimal)
t = 2 years
Let's assume the principal sum is P.
Given that the compound interest is Rs 170, we can rewrite the formula as:
A = P + 170
Now, let's substitute the values into the formula:
P + 170 = P(1 + 0.125/1)^(1*2)
Simplifying further:
P + 170 = P(1.125)^2
P + 170 = P(1.265625)
Now, let's solve for P by isolating it on one side of the equation:
P(1.265625) - P = 170
P(0.265625) = 170
Dividing both sides of the equation by 0.265625:
P = 170 / 0.265625
P = 640
Therefore, the sum is Rs 640.
Hence, option C (640) is the correct answer.
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal sum (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we are given:
r = 12(1/2)% per annum = 12.5% = 0.125 (as a decimal)
t = 2 years
Let's assume the principal sum is P.
Given that the compound interest is Rs 170, we can rewrite the formula as:
A = P + 170
Now, let's substitute the values into the formula:
P + 170 = P(1 + 0.125/1)^(1*2)
Simplifying further:
P + 170 = P(1.125)^2
P + 170 = P(1.265625)
Now, let's solve for P by isolating it on one side of the equation:
P(1.265625) - P = 170
P(0.265625) = 170
Dividing both sides of the equation by 0.265625:
P = 170 / 0.265625
P = 640
Therefore, the sum is Rs 640.
Hence, option C (640) is the correct answer.
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Compound interest on a certain sum for 2 years at 12(1/2)% per annum is Rs 170. Find the sum.a)345b)740c)640d)525Correct answer is option 'C'. Can you explain this answer?
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