Problem regarding simple interest

[Benjamin_harsh]

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%?

 

[mitochan]

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$.

 

[SammyS]

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.

 

[HallsofIvy]

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.