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A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.?
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A sum of money at simple interest doubles itself in 8 years 4 months. ...
Introduction:
In this problem, we are given that a certain sum of money doubles itself in 8 years and 4 months at a simple interest rate. We need to determine the time it will take for the same sum of money to triple itself.
Given:
- The sum of money doubles itself in 8 years and 4 months.
- Simple interest is used to calculate the growth of the sum of money.
- We need to find the time it will take for the sum of money to triple itself.
Approach:
To solve this problem, we will use the concept of simple interest and the formula to calculate the amount of money after a certain period of time.
Step 1: Calculate the interest rate per year:
To calculate the interest rate per year, we can use the formula:
Interest = Principal * Rate * Time
Since the interest is equal to the principal (initial sum of money) after 8 years and 4 months, we can write:
Interest = Principal
So, Principal * Rate * Time = Principal
Simplifying this equation, we have:
Rate * Time = 1
Step 2: Calculate the time it takes for the sum to triple:
To calculate the time it takes for the sum to triple, we can use the formula:
Amount = Principal + Interest
Since the interest is equal to the principal, we can write:
Amount = Principal + Principal
Amount = 2 * Principal
Similarly, when the sum triples, we can write:
Amount = 3 * Principal
Therefore, the time it takes for the sum to triple can be calculated using the formula:
Time = Amount / (Principal * Rate)
Substituting the values, we have:
Time = (3 * Principal) / (Principal * Rate)
Step 3: Solve for time:
Using the equation derived in Step 1 (Rate * Time = 1), we can substitute the value of Time in the formula derived in Step 2:
Time = (3 * Principal) / (Principal * Rate)
Time = (3 * Principal) / (Principal * (1 / Time))
Simplifying this equation, we have:
Time = 3 / (1 / Time)
Cross-multiplying the equation, we get:
Time * (1 / Time) = 3
Simplifying further, we have:
1 = 3
Therefore, the time it takes for the sum to triple itself is 1 year.
Conclusion:
The sum of money will triple itself in 1 year.
In this problem, we are given that a certain sum of money doubles itself in 8 years and 4 months at a simple interest rate. We need to determine the time it will take for the same sum of money to triple itself.
Given:
- The sum of money doubles itself in 8 years and 4 months.
- Simple interest is used to calculate the growth of the sum of money.
- We need to find the time it will take for the sum of money to triple itself.
Approach:
To solve this problem, we will use the concept of simple interest and the formula to calculate the amount of money after a certain period of time.
Step 1: Calculate the interest rate per year:
To calculate the interest rate per year, we can use the formula:
Interest = Principal * Rate * Time
Since the interest is equal to the principal (initial sum of money) after 8 years and 4 months, we can write:
Interest = Principal
So, Principal * Rate * Time = Principal
Simplifying this equation, we have:
Rate * Time = 1
Step 2: Calculate the time it takes for the sum to triple:
To calculate the time it takes for the sum to triple, we can use the formula:
Amount = Principal + Interest
Since the interest is equal to the principal, we can write:
Amount = Principal + Principal
Amount = 2 * Principal
Similarly, when the sum triples, we can write:
Amount = 3 * Principal
Therefore, the time it takes for the sum to triple can be calculated using the formula:
Time = Amount / (Principal * Rate)
Substituting the values, we have:
Time = (3 * Principal) / (Principal * Rate)
Step 3: Solve for time:
Using the equation derived in Step 1 (Rate * Time = 1), we can substitute the value of Time in the formula derived in Step 2:
Time = (3 * Principal) / (Principal * Rate)
Time = (3 * Principal) / (Principal * (1 / Time))
Simplifying this equation, we have:
Time = 3 / (1 / Time)
Cross-multiplying the equation, we get:
Time * (1 / Time) = 3
Simplifying further, we have:
1 = 3
Therefore, the time it takes for the sum to triple itself is 1 year.
Conclusion:
The sum of money will triple itself in 1 year.
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A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.?
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A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.?.
A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money at simple interest doubles itself in 8 years 4 months. In how much time will it treble itself.?.
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