Question

Gabriel asked to borrow $420 from his roommate John to purchase new electronics after his laptop stopped working. John agreed and told Gabriel that they could figure out an interest rate later. Gabriel paid John a total of $426.93 at the end of six months. What was the simple annual interest rate that Gabriel ended up paying his roommate.

Answer 1

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;

`\text{Simple interest = }\frac{P\text{ }*\text{ R }*\text{ T}}{100}`

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;

`\begin{gathered} \text{Rate = }\frac{100\text{ }*\text{ simple interest}}{P\text{ }*\text{ T}} \\ \\ \text{Rate = }\frac{100\text{ }*\text{ 26.93}}{420\text{ }*\text{ 0.5}} \\ \\ \text{Rate = }(2693)/(210) \\ \\ \text{Rate = 12.82 percent} \end{gathered}`