Respuesta :
The simple annual interest rate Gabriel ended up paying his roommate is 12.82%
Here, we want to calculate the interest rate paid by Gabriel to his roommate John.
Mathematically, the formula for simple interest is as follows;
[tex]\text{Simple interest = }\frac{P\text{ }\times\text{ R }\times\text{ T}}{100}[/tex]Where P is the principal which represents the amount borrowed which is $420
R is the interest rate which we are trying to calculate
T is the time frame which is 6 months according to the question. In this case we represent the months by dividing by 12 which is 6/12 = 0.5
The simple interest is also the difference between the amount borrowed and the amount paid back.
In this case, the simple interest will be $426.93 - $420 = $26.93
Since it is the rate we are trying to calculate, we can make it the subject of the formula. Thus;
[tex]\begin{gathered} \text{Rate = }\frac{100\text{ }\times\text{ simple interest}}{P\text{ }\times\text{ T}} \\ \\ \text{Rate = }\frac{100\text{ }\times\text{ 26.93}}{420\text{ }\times\text{ 0.5}} \\ \\ \text{Rate = }\frac{2693}{210} \\ \\ \text{Rate = 12.82 percent} \end{gathered}[/tex]