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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? solve?
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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
Given Data
- Rate of Interest = 12.5% p.a.
- Time = 2 years
- Difference between CI and SI = Rs. 435
Calculating Simple Interest for 2 Years
- SI for 2 years:
SI = (X × 12.5 × 2) / 100
SI = (25X) / 100
SI = 0.25X
Calculating Compound Interest for 2 Years
- CI for 2 years:
CI = X × (1 + 12.5/100)^2 - X
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:
0.265625X - 0.25X = Rs. 435
0.015625X = 435
Calculating the Value of X
- To find X:
X = 435 / 0.015625
X = 27840
Conclusion
The value of X is Rs. 27,840. This amount, when invested at an interest rate of 12.5% per annum, results in a difference of Rs. 435 between the compound interest and simple interest over two years.
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
Given Data
- Rate of Interest = 12.5% p.a.
- Time = 2 years
- Difference between CI and SI = Rs. 435
Calculating Simple Interest for 2 Years
- SI for 2 years:
SI = (X × 12.5 × 2) / 100
SI = (25X) / 100
SI = 0.25X
Calculating Compound Interest for 2 Years
- CI for 2 years:
CI = X × (1 + 12.5/100)^2 - X
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:
0.265625X - 0.25X = Rs. 435
0.015625X = 435
Calculating the Value of X
- To find X:
X = 435 / 0.015625
X = 27840
Conclusion
The value of X is Rs. 27,840. This amount, when invested at an interest rate of 12.5% per annum, results in a difference of Rs. 435 between the compound interest and simple interest over two years.
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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? solve?
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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? solve? 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? solve? 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? solve?.
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? solve? 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? solve? 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? solve?.
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