Question

Express the given quantity in terms of the indicated variable.

The interest obtains after 1 year on investment at $2\frac{1}{2}\%$simple interest per year; x = number of dollars invested.

Short answer

The simple interest is $I=0.125x$.

Step-by-step solution

Step 1. Definition of simple interest formula.

Simple interest is a method of calculating interest based on the original amount invested or loaned called the principal. The annual interest is given by $I=Prt$where P is the principal amount invested or borrowed, r is the interest rate andt is the number of year elapsed.

Step 2. Plug the values in the formula.

Here,$P=x$

$\begin{array}{l}r=2\frac{1}{2}\%\\ =\frac{5}{2}\%\\ =\frac{5}{2\times 100}\\ =\frac{5}{200}\\ =0.025\end{array}$

$t=1$

Plug the values in the simple interest formula:

$I=x\left(0.125\right)\cdot 1$

Step 3. Calculate simple interest.

Multiply

$\begin{array}{l}I=x\left(0.125\right)\cdot 1\\ I=0.125x\end{array}$