Question

Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesperson indicated that the price of the car was either \(27,600 cash or \)6,900 at the end of each of 5 years. Compute the effective-interest rate to the nearest percent that Glenda would pay if she chooses to make the five annual payments.

Short answer

The effective interest rate that Glenda would pay will be 8% approximately.

Step-by-step solution

Definition of effective interest rate

Effective interest rate is defined as the annual interest on savings when the effect of compounding over time.

Calculation of the effective interest rate.

$\begin{array}{rcl}\mathbf{27}\mathbf{,}\mathbf{600}\mathbf{}& \mathbf{=}& \mathbf{}\mathit{P}\mathit{V}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{a}\mathit{n}\mathbf{}\mathit{o}\mathit{r}\mathit{d}\mathit{i}\mathit{n}\mathit{a}\mathit{r}\mathit{y}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{900}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{f}\mathit{i}\mathit{v}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{o}\mathit{d}\mathit{s}\mathbf{}\mathit{a}\mathit{t}\mathbf{}\mathbf{?}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\\ \frac{\mathbf{27}\mathbf{,}\mathbf{600}}{\mathbf{6}\mathbf{,}\mathbf{900}}& \mathbf{=}& \mathbf{}\mathit{P}\mathit{V}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{o}\mathit{r}\mathit{d}\mathit{i}\mathit{n}\mathit{a}\mathit{r}\mathit{y}\mathbf{}\mathit{a}\mathit{n}\mathit{n}\mathit{u}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathit{f}\mathit{i}\mathit{v}\mathit{e}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{o}\mathit{d}\mathit{s}\mathbf{}\mathit{a}\mathit{t}\mathbf{}\mathbf{?}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\\ \mathbf{4}\mathbf{.}\mathbf{0}\mathbf{}& \mathbf{=}& \mathbf{}\mathit{a}\mathit{p}\mathit{p}\mathit{r}\mathit{o}\mathit{x}\mathit{i}\mathit{m}\mathit{a}\mathit{t}\mathit{e}\mathit{l}\mathit{y}\mathbf{}\mathbf{8}\mathbf{\%}\mathbf{}\end{array}$