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Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?
- a)14%
- b)16%
- c)12.5%
- d)15%
- e)15.5%
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Difference between the compound interest and the simple interest accru...
Let the rate be R% p.a. Then,
Rate = 15%.
Rate = 15%.
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Difference between the compound interest and the simple interest accru...
Difference between compound interest and simple interest
The difference between compound interest and simple interest can be calculated using the formula:
Difference = Compound Interest - Simple Interest
Where,
Compound Interest = P(1 + r/n)^(nt) - P
Simple Interest = P * r * t
Given:
Principal amount (P) = Rs. 18000
Difference (Compound Interest - Simple Interest) = Rs. 405
Time (t) = 2 years
To find the rate of interest (r), we can substitute the given values into the formula and solve for r.
Calculating Compound Interest
Compound Interest = P(1 + r/n)^(nt) - P
In this case, the interest is compounded annually (n = 1), so the formula becomes:
Compound Interest = P(1 + r)^t - P
Substituting the given values:
Compound Interest = 18000(1 + r)^2 - 18000
Calculating Simple Interest
Simple Interest = P * r * t
Substituting the given values:
Simple Interest = 18000 * r * 2
Calculating the Difference
Difference = Compound Interest - Simple Interest
Substituting the calculated values:
405 = 18000(1 + r)^2 - 18000 - 18000 * r * 2
Simplifying the equation:
405 = 18000[(1 + r)^2 - 1 - 2r]
405 = 18000(1 + r)^2 - 18000 - 36000r
405 = 18000(1 + 2r + r^2) - 18000 - 36000r
405 = 18000 + 36000r + 18000r^2 - 18000 - 36000r
405 = 18000r^2
18000r^2 = 405
r^2 = 405/18000
r^2 = 9/400
Taking the square root of both sides:
r = √(9/400)
r = 3/20
r = 0.15
Converting to percentage
The rate of interest is calculated as a decimal value, so we need to convert it to a percentage:
Rate of interest = 0.15 * 100
Rate of interest = 15%
Therefore, the rate of interest is 15%.
The difference between compound interest and simple interest can be calculated using the formula:
Difference = Compound Interest - Simple Interest
Where,
Compound Interest = P(1 + r/n)^(nt) - P
Simple Interest = P * r * t
Given:
Principal amount (P) = Rs. 18000
Difference (Compound Interest - Simple Interest) = Rs. 405
Time (t) = 2 years
To find the rate of interest (r), we can substitute the given values into the formula and solve for r.
Calculating Compound Interest
Compound Interest = P(1 + r/n)^(nt) - P
In this case, the interest is compounded annually (n = 1), so the formula becomes:
Compound Interest = P(1 + r)^t - P
Substituting the given values:
Compound Interest = 18000(1 + r)^2 - 18000
Calculating Simple Interest
Simple Interest = P * r * t
Substituting the given values:
Simple Interest = 18000 * r * 2
Calculating the Difference
Difference = Compound Interest - Simple Interest
Substituting the calculated values:
405 = 18000(1 + r)^2 - 18000 - 18000 * r * 2
Simplifying the equation:
405 = 18000[(1 + r)^2 - 1 - 2r]
405 = 18000(1 + r)^2 - 18000 - 36000r
405 = 18000(1 + 2r + r^2) - 18000 - 36000r
405 = 18000 + 36000r + 18000r^2 - 18000 - 36000r
405 = 18000r^2
18000r^2 = 405
r^2 = 405/18000
r^2 = 9/400
Taking the square root of both sides:
r = √(9/400)
r = 3/20
r = 0.15
Converting to percentage
The rate of interest is calculated as a decimal value, so we need to convert it to a percentage:
Rate of interest = 0.15 * 100
Rate of interest = 15%
Therefore, the rate of interest is 15%.
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Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?a)14%b)16%c)12.5%d)15%e)15.5%Correct answer is option 'D'. Can you explain this answer?
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Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?a)14%b)16%c)12.5%d)15%e)15.5%Correct answer is option 'D'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?a)14%b)16%c)12.5%d)15%e)15.5%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?a)14%b)16%c)12.5%d)15%e)15.5%Correct answer is option 'D'. Can you explain this answer?.
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