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The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X?
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The difference between the simple interest and compound interest on a ...
Understanding Simple Interest and Compound Interest
Simple Interest (SI) is calculated using the formula:
SI = (Principal * Rate * Time) / 100
Compound Interest (CI) is calculated using the formula:
CI = Principal * (1 + Rate/100)^Time - Principal
In this problem, we need to find the principal amount (Rs. X) for which the difference between the compound interest and simple interest for two years at a rate of 12.5% p.a. is Rs. 435.
Calculating Simple Interest for 2 Years
- Rate = 12.5%
- Time = 2 years
Using the SI formula:
SI = (X * 12.5 * 2) / 100
SI = (25X) / 100
SI = 0.25X
Calculating Compound Interest for 2 Years
Using the CI formula:
CI = X * (1 + 0.125)^2 - X
CI = X * (1.125)^2 - X
CI = X * (1.265625) - X
CI = 0.265625X
Finding the Difference
The difference between CI and SI is given as Rs. 435:
CI - SI = 435
0.265625X - 0.25X = 435
0.015625X = 435
Calculating the Value of X
To find X, we rearrange the equation:
X = 435 / 0.015625
X = 27,840
Conclusion
The value of X, the principal amount, is Rs. 27,840. This demonstrates the difference between simple and compound interest effectively over a two-year period.
Simple Interest (SI) is calculated using the formula:
SI = (Principal * Rate * Time) / 100
Compound Interest (CI) is calculated using the formula:
CI = Principal * (1 + Rate/100)^Time - Principal
In this problem, we need to find the principal amount (Rs. X) for which the difference between the compound interest and simple interest for two years at a rate of 12.5% p.a. is Rs. 435.
Calculating Simple Interest for 2 Years
- Rate = 12.5%
- Time = 2 years
Using the SI formula:
SI = (X * 12.5 * 2) / 100
SI = (25X) / 100
SI = 0.25X
Calculating Compound Interest for 2 Years
Using the CI formula:
CI = X * (1 + 0.125)^2 - X
CI = X * (1.125)^2 - X
CI = X * (1.265625) - X
CI = 0.265625X
Finding the Difference
The difference between CI and SI is given as Rs. 435:
CI - SI = 435
0.265625X - 0.25X = 435
0.015625X = 435
Calculating the Value of X
To find X, we rearrange the equation:
X = 435 / 0.015625
X = 27,840
Conclusion
The value of X, the principal amount, is Rs. 27,840. This demonstrates the difference between simple and compound interest effectively over a two-year period.
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The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X?
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The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X? for Bank Exams 2025 is part of Bank Exams preparation. The Question and answers have been prepared according to the Bank Exams exam syllabus. Information about The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X? covers all topics & solutions for Bank Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X?.
The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X? for Bank Exams 2025 is part of Bank Exams preparation. The Question and answers have been prepared according to the Bank Exams exam syllabus. Information about The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X? covers all topics & solutions for Bank Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the simple interest and compound interest on a sum of Rs. X for two years at the rate of 12.5% p.a. is Rs. 435. What is the value of X?.
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