Problem regarding simple interest

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In summary, the given conversation discusses a problem in which a sum of money doubles itself in 7 years at simple interest. The solution shows that after 21 years, the amount will become 4 times the original amount, with a total interest of 300%. This is because after 7 years, the amount earns 100% interest, and after another 7 years, it earns another 100% interest, resulting in a total of 300% interest over 21 years. This is in contrast to compound interest, where the amount would double in 14 years.
  • #1
Benjamin_harsh
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Homework Statement
A sum of money doubles itself in 7 yrs at Simple Interest . In how many years it will become 4 times?
Relevant Equations
7yr=100% interest
21yr=300% interest
Amount=(100+300)%=400%=4 times of principal
7yr=100% interest
21yr=300% interest
Amount=(100+300)%=400%=4 times of principal

How 7 years is equal to 100% interest?

Why in last step, we added 100% & 300%?
 
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  • #2
First 100$ becomes 100$ + 100$ interest after 7 yrs.
First 100$ becomes 100$ + 100$ interest + 100$ new interest after next 7 yrs.
First 100$ becomes 100$ + 100$ interest + 100$ interest + 100$ new interest after further next 7 yrs.
So after 21 yrs we get total amount of money of 400$ including total amount of interest 300$.
 
  • #3
Benjamin_harsh said:
Homework Statement:: A sum of money doubles itself in 7 yrs at Simple Interest . In how many years it will become 4 times?
Homework Equations:: 7yr=100% interest
21yr=300% interest
Amount=(100+300)%=400%=4 times of principal

7yr=100% interest
21yr=300% interest
Amount=(100+300)%=400%=4 times of principal

How 7 years is equal to 100% interest?

Why in last step, we added 100% & 300%?
You need to make clear what you're asking about.

It looks like you are showing a solution that's been given to you, and you want some part (or parts) of the solution explained.

Now, regarding some of your questions:
Of course the equation, " 7yr=100% interest ", is not true in a literal sense. It likely refers to the fact that over the course of 7 years, the amount of interest earned is equal to the initial principal, making that amount of interest equal to 100% of the principle.
 
  • #4
It is important that this is SIMPLE interest. Taking the original amount to be P, since it doubles in 7 years, it has earned P interest in 7 years. In another 7 years, a total of 14 years, it will earn another P interest so now will be worth 3P. In yet another 7 years, a total of 21 years, it will earn another P interest so now will be worth 4P. The answer is 21 years.

If this had been compound interest, the answer would be 14 years. Since the principle doubled in 7 years, with compound interest, in another it will double again to 4 times the original amount.
 

FAQ: Problem regarding simple interest

1. What is simple interest and how is it calculated?

Simple interest is a type of interest that is calculated as a percentage of the principal amount borrowed or invested. It does not take into account any additional factors such as compounding. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the interest rate, and T is the time period.

2. What are some real-life examples of simple interest?

Simple interest is commonly used in situations such as loans, where a borrower pays back the principal amount plus the interest at a specified rate over a period of time. It is also used in savings accounts, where the bank pays the account holder a certain percentage of interest on their deposited funds.

3. What is the difference between simple interest and compound interest?

The main difference between simple interest and compound interest is that simple interest only applies to the principal amount, while compound interest takes into account both the principal and any accumulated interest. This means that compound interest will result in a higher overall amount compared to simple interest.

4. How does the time period affect simple interest?

The longer the time period, the more interest will be accrued with simple interest. This is because the interest is calculated as a percentage of the principal amount, and the longer the time period, the more times the interest will be applied. This is why it is important to pay off loans or invest for a shorter period of time to minimize the amount of interest paid.

5. Can simple interest be negative?

Yes, it is possible for simple interest to be negative. This occurs when the interest rate is negative, meaning that the borrower or investor actually receives money instead of paying it. This is not common, but can happen in certain economic situations.

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