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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...
Difference of CI and SI in 2 years = Pr2/(100)2
r2 = 15%
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Difference between the compound interest and the simple interest accru...
Difference between compound interest and simple interest:
Compound interest and simple interest are two different methods of calculating the interest accrued on a principal amount. The main difference between these two methods lies in the way the interest is calculated and added to the principal.
Simple Interest:
Simple interest is calculated by multiplying the principal amount, the rate of interest, and the time period. The formula for calculating simple interest is:
Simple Interest = (Principal * Rate * Time) / 100
Compound Interest:
Compound interest is calculated by adding the interest earned at the end of each compounding period to the principal amount, and then calculating the interest for the next period based on the increased principal. The formula for calculating compound interest is:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Given Information:
Principal amount (P) = Rs. 18000
Time (T) = 2 years
Difference between compound interest and simple interest = Rs. 405
Solution:
To find the rate of interest, we need to equate the difference between compound interest and simple interest to Rs. 405 and solve for the rate.
Let's calculate the compound interest and simple interest first.
Simple Interest:
Simple Interest = (Principal * Rate * Time) / 100
405 = (18000 * R * 2) / 100
40500 = 360 * R
R = 40500 / 360
R = 112.5
Compound Interest:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Compound Interest = 18000 * (1 + R/100)^2 - 18000
405 = 18000 * (1 + 112.5/100)^2 - 18000
405 = 18000 * (2.125)^2 - 18000
405 = 18000 * 4.515625 - 18000
405 = 81182.5 - 18000
405 = 63182.5
The above calculation shows that the compound interest is not equal to Rs. 405. Hence, there is an error in the given question.
However, if we assume that the difference between compound interest and simple interest is Rs. 315 instead of Rs. 405, we can calculate the rate of interest.
Simple Interest:
Simple Interest = (Principal * Rate * Time) / 100
315 = (18000 * R * 2) / 100
31500 = 360 * R
R = 31500 / 360
R = 87.5
Compound Interest:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Compound Interest = 18000 * (1 + R/100)^2 - 18000
315 = 18000 * (1 + 87.5/100)^2 - 18000
315 = 18000 * (1.875)^2 - 18000
315 = 18000 * 3.515625 - 18000
315 = 63094.6875 - 18000
315 = 45094.6875
Since the compound interest is not equal to Rs. 315, we can conclude that there is an error in
Compound interest and simple interest are two different methods of calculating the interest accrued on a principal amount. The main difference between these two methods lies in the way the interest is calculated and added to the principal.
Simple Interest:
Simple interest is calculated by multiplying the principal amount, the rate of interest, and the time period. The formula for calculating simple interest is:
Simple Interest = (Principal * Rate * Time) / 100
Compound Interest:
Compound interest is calculated by adding the interest earned at the end of each compounding period to the principal amount, and then calculating the interest for the next period based on the increased principal. The formula for calculating compound interest is:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Given Information:
Principal amount (P) = Rs. 18000
Time (T) = 2 years
Difference between compound interest and simple interest = Rs. 405
Solution:
To find the rate of interest, we need to equate the difference between compound interest and simple interest to Rs. 405 and solve for the rate.
Let's calculate the compound interest and simple interest first.
Simple Interest:
Simple Interest = (Principal * Rate * Time) / 100
405 = (18000 * R * 2) / 100
40500 = 360 * R
R = 40500 / 360
R = 112.5
Compound Interest:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Compound Interest = 18000 * (1 + R/100)^2 - 18000
405 = 18000 * (1 + 112.5/100)^2 - 18000
405 = 18000 * (2.125)^2 - 18000
405 = 18000 * 4.515625 - 18000
405 = 81182.5 - 18000
405 = 63182.5
The above calculation shows that the compound interest is not equal to Rs. 405. Hence, there is an error in the given question.
However, if we assume that the difference between compound interest and simple interest is Rs. 315 instead of Rs. 405, we can calculate the rate of interest.
Simple Interest:
Simple Interest = (Principal * Rate * Time) / 100
315 = (18000 * R * 2) / 100
31500 = 360 * R
R = 31500 / 360
R = 87.5
Compound Interest:
Compound Interest = Principal * (1 + Rate/100)^Time - Principal
Compound Interest = 18000 * (1 + R/100)^2 - 18000
315 = 18000 * (1 + 87.5/100)^2 - 18000
315 = 18000 * (1.875)^2 - 18000
315 = 18000 * 3.515625 - 18000
315 = 63094.6875 - 18000
315 = 45094.6875
Since the compound interest is not equal to Rs. 315, we can conclude that there is an error in
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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?.
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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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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
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