# How X + X = 2X step written? "Amount invested w/ simple interest doubles itself..."

#### Ganesh Ujwal

##### New member
How X + X = 2X step written? "Amount invested w/ simple interest doubles itself..."

Question: A certain amount put a simple interest doubles itself after 4.5 years. In how much time would the amount become four times of itself?
In this Video I am having trouble in understanding.
How X + X = 2X step written?

I know SI = PRT / 100

#### Dr.Peterson

##### Elite Member
Question: A certain amount put a simple interest doubles itself after 4.5 years. In how much time would the amount become four times of itself?
In this Video I am having trouble in understanding.
How X + X = 2X step written?

I know SI = PRT / 100
What do you mean by "how"? You can see it being written, with the second "x" being written last. This is because we start with x (the principal) and end up with 2x, so the interest added is x.

In talking about simple interest, we need to focus on the interest, not the final amount, which includes the principal. In effect, he is using the fact that A = P + I (that is, the final amount is the principal plus the interest), so that I = A - P. Here the final amount is 2x, and the principal is x, so the interest must be 2x - x = x.

I have to say that my immediate answer was 9 years; that is because I naturally expect compound interest in a question like this, so that the interest for the next 4.5 years would be 2x and the new amount 4x (that is, the amount doubles every 4.5 years). But this is simple interest; to end up with 4x, we need interest of 3x. Simple interest adds; compound interest multiplies.

#### Denis

##### Senior Member
Can be done this way:

step 1: 1 grows to 2 in 4.5 periods, so 1/4.5 per period.

step 2: 2 grows to 4 in 2/(1/4.5) = 9 periods