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If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be?
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If the difference between the simple interest and compound interest on...
Difference between Simple Interest and Compound Interest
To find the principle amount, we need to understand the concept of simple interest and compound interest, as well as the formula to calculate both.
Simple Interest: Simple interest is calculated as a percentage of the principal amount over a certain period of time. The formula for simple interest is:
Simple Interest = (Principal Amount * Rate * Time) / 100
Compound Interest: Compound interest is calculated on both the principal amount and the accumulated interest from previous periods. The formula for compound interest is:
Compound Interest = Principal Amount * (1 + Rate/100)^Time - Principal Amount
Given Information
The given information in the question is as follows:
Rate = 20%
Time = 3 years
Difference between Simple Interest and Compound Interest = 48
Calculating Simple Interest
Using the formula for simple interest, we can calculate the simple interest for 3 years at a rate of 20% per annum:
Simple Interest = (Principal Amount * Rate * Time) / 100
Calculating Compound Interest
Using the formula for compound interest, we can calculate the compound interest for 3 years at a rate of 20% per annum:
Compound Interest = Principal Amount * (1 + Rate/100)^Time - Principal Amount
Finding the Principle Amount
We need to find the principle amount based on the given difference between simple interest and compound interest, which is 48.
To find the principle amount, we can set up an equation:
Simple Interest - Compound Interest = 48
Replacing the formulas for simple interest and compound interest, we get:
(Principal Amount * Rate * Time) / 100 - (Principal Amount * (1 + Rate/100)^Time - Principal Amount) = 48
Simplifying the equation, we get:
(Principal Amount * Rate * Time) / 100 - Principal Amount * (1 + Rate/100)^Time + Principal Amount = 48
Factoring out the common term of Principal Amount, we get:
Principal Amount * [(Rate * Time) / 100 - (1 + Rate/100)^Time + 1] = 48
Now, we can solve this equation to find the principle amount.
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If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be?
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If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be?.
If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the simple interest and compound interest on some principle amount at 20%per annum for 3 year is 48 then the principle amount must be?.
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