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The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
- a)9%
- b)12%
- c)8%
- d)6%
Correct answer is option 'C'. Can you explain this answer?
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To find the rate of interest per annum, we need to first calculate the simple interest and compound interest for 2 years and then find the difference between them.
Given:
Principal amount (P) = Rs. 15,000
Difference between compound interest and simple interest (CI - SI) = Rs. 96
Time (T) = 2 years
Let's calculate the simple interest first:
Simple Interest (SI) = (P * R * T) / 100
Where R is the rate of interest.
Substituting the given values, we have:
96 = (15,000 * R * 2) / 100
96 = 300 * R
R = 96 / 300
R = 0.32
So, the rate of interest for simple interest is 0.32 or 0.32%.
Now, let's calculate the compound interest:
Compound Interest (CI) = P * (1 + R/100)^T - P
Substituting the given values, we have:
CI = 15,000 * (1 + 0.32/100)^2 - 15,000
CI = 15,000 * (1 + 0.0032)^2 - 15,000
CI = 15,000 * (1.0032)^2 - 15,000
CI = 15,000 * 1.0064 - 15,000
CI = 15,096 - 15,000
CI = 96
So, the compound interest is also Rs. 96.
Since the difference between compound interest and simple interest is Rs. 96, we can conclude that the rate of interest for compound interest is the same as the rate of interest for simple interest.
Hence, the rate of interest per annum is 0.32% or 0.32, which is approximately 0.32%. Therefore, the correct option is c) 8%.
Given:
Principal amount (P) = Rs. 15,000
Difference between compound interest and simple interest (CI - SI) = Rs. 96
Time (T) = 2 years
Let's calculate the simple interest first:
Simple Interest (SI) = (P * R * T) / 100
Where R is the rate of interest.
Substituting the given values, we have:
96 = (15,000 * R * 2) / 100
96 = 300 * R
R = 96 / 300
R = 0.32
So, the rate of interest for simple interest is 0.32 or 0.32%.
Now, let's calculate the compound interest:
Compound Interest (CI) = P * (1 + R/100)^T - P
Substituting the given values, we have:
CI = 15,000 * (1 + 0.32/100)^2 - 15,000
CI = 15,000 * (1 + 0.0032)^2 - 15,000
CI = 15,000 * (1.0032)^2 - 15,000
CI = 15,000 * 1.0064 - 15,000
CI = 15,096 - 15,000
CI = 96
So, the compound interest is also Rs. 96.
Since the difference between compound interest and simple interest is Rs. 96, we can conclude that the rate of interest for compound interest is the same as the rate of interest for simple interest.
Hence, the rate of interest per annum is 0.32% or 0.32, which is approximately 0.32%. Therefore, the correct option is c) 8%.
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