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If the difference between the compound interest and simple interest on a certain sum at 5% per annum for 3 years is Rs. 15·25, what is the sum ?
- a)Rs. 2000
- b)Rs. 1000
- c)Rs. 2500
- d)Rs. 1500
Correct answer is option 'A'. Can you explain this answer?
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To solve this problem, we can use the formula for compound interest:
Compound Interest = P(1 + r/n)^(nt) - P
Where:
P = principal amount (initial sum)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
We are given that the annual interest rate is 5% (r = 0.05) and the time is 3 years (t = 3). Let's assume the principal amount is P.
The compound interest for 3 years at 5% per annum can be calculated as:
Compound Interest = P(1 + 0.05/1)^(1*3) - P
The simple interest for 3 years at 5% per annum can be calculated as:
Simple Interest = P * 0.05 * 3
According to the problem, the difference between the compound interest and simple interest is Rs. 15. Therefore:
Compound Interest - Simple Interest = 15
[P(1 + 0.05/1)^(1*3) - P] - (P * 0.05 * 3) = 15
Simplifying the equation:
P(1.05^3 - 1) - P * 0.15 = 15
P * (1.157625 - 1 - 0.15) = 15
P * 0.007625 = 15
Dividing both sides by 0.007625:
P = 15 / 0.007625
P ≈ 1967.5
Therefore, the principal amount is approximately Rs. 1967.5.
Compound Interest = P(1 + r/n)^(nt) - P
Where:
P = principal amount (initial sum)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
We are given that the annual interest rate is 5% (r = 0.05) and the time is 3 years (t = 3). Let's assume the principal amount is P.
The compound interest for 3 years at 5% per annum can be calculated as:
Compound Interest = P(1 + 0.05/1)^(1*3) - P
The simple interest for 3 years at 5% per annum can be calculated as:
Simple Interest = P * 0.05 * 3
According to the problem, the difference between the compound interest and simple interest is Rs. 15. Therefore:
Compound Interest - Simple Interest = 15
[P(1 + 0.05/1)^(1*3) - P] - (P * 0.05 * 3) = 15
Simplifying the equation:
P(1.05^3 - 1) - P * 0.15 = 15
P * (1.157625 - 1 - 0.15) = 15
P * 0.007625 = 15
Dividing both sides by 0.007625:
P = 15 / 0.007625
P ≈ 1967.5
Therefore, the principal amount is approximately Rs. 1967.5.
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If the difference between the compound interest and simple interest on a certain sum at 5% per annum for 3 years is Rs. 15·25, what is the sum ?a)Rs. 2000b)Rs. 1000c)Rs. 2500d)Rs. 1500Correct answer is option 'A'. Can you explain this answer?
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