Q51. - Algebra 1

Question

Zita’s computer is depreciating at a rate of $\mathbf{3}\mathit{\%}$ per year. She bought the computer for $\mathit{\$}\mathbf{1200}$.

a. Write an equation to represent this situation.

b. What will the computer’s value be after 5 years?

Step-by-Step Solution

Answer

a. The equation that represents the situation is $\mathbf{3}\mathit{\%}$ $\mathit{A}\mathbf{=}\mathbf{1200}\mathbf{\times }{\mathbf{\left(}\mathbf{0.97}\mathbf{\right)}}^{\mathbf{t}}$.

b. The final value of the computer after 5 years will be $\mathit{\$}\mathbf{1030.48}$.

Step 1. Write the compound interest equation.

The compound interest equation is given by:

$A=P{\left(1+\frac{r}{n}\right)}^{nt}$, where $A$ is the amount, $P$ is the principal amount, $r$ is the rate of interest, $t$ is the time.

Step 2. Substitute the values.

Zita bought a computer for $\$1200$ which is depreciating at a rate of $3\%$ per year i.e., the rate of interest must be $-3\%$. 

To find the equation that represents the situation substitute 1200 for $P$, 1 for $n$, and $-3\%$ for $r$ into the formula $A=P{\left(1+\frac{{\displaystyle r}}{{\displaystyle n}}\right)}^{nt}$.

$\begin{array}{c}\text{A}=P{\left(1+\frac{r}{n}\right)}^{n.t}\\ =1200\times {(1-\frac{0.03}{1})}^{1\times t}\end{array}$