Question

Postal Express has outlets throughout the world. It also keeps funds for transactions purposes in many foreign countries. Assume in 2010 it held 240,000 reals in Brazil worth 170,000 dollars. It drew 12 percent interest, but the Brazilian real declined 24 percent against the dollar.

a. What is the value of its holdings, based on U.S. dollars, at year-end? (Hint: Multiply $170,000 times 1.12 and then multiply the resulting value by 76 percent.)

Short answer

The year-end value of the holding will be $144,614.

Step-by-step solution

Information provided in question

Value of 240,000 reals in 2010 = $170,000

Interest drawn by the funds = 12%

Percentage decrease in value of real against dollars = 24%

Calculation of the value of the holdings

The value of the holdings at year-end will be $144,614.

$\begin{array}{rcl}\mathit{S}\mathit{p}\mathit{o}\mathit{t}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}& \mathbf{=}& \frac{\mathbf{Dollars}}{\mathbf{Reals}}\\ & \mathbf{=}& \frac{\mathbf{170}\mathbf{,}\mathbf{000}}{\mathbf{240}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{7084}\end{array}$

$\begin{array}{rcl}\mathit{Y}\mathit{e}\mathit{a}\mathit{r}\mathbf{-}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}& \mathbf{=}& \mathit{S}\mathit{p}\mathit{o}\mathit{t}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{Decrease}\mathbf{}\mathbf{in}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{real}\mathbf{)}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{7084}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{24}\mathbf{)}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{538}\end{array}$

$\begin{array}{rcl}\mathit{D}\mathit{e}\mathit{p}\mathit{o}\mathit{s}\mathit{i}\mathit{t}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{r}\mathit{e}\mathit{a}\mathit{l}\mathbf{}\mathit{a}\mathit{f}\mathit{t}\mathit{e}\mathit{r}\mathbf{}\mathbf{1}\mathbf{}\mathit{y}\mathit{e}\mathit{a}\mathit{r}& \mathbf{=}& \mathit{I}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{a}\mathit{l}\mathbf{}\mathit{d}\mathit{e}\mathit{p}\mathit{o}\mathit{s}\mathit{i}\mathit{t}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{Interest}\mathbf{}\mathbf{rate}\mathbf{)}\\ & \mathbf{=}& \mathbf{240}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{)}\\ & \mathbf{=}& \mathbf{268}\mathbf{,}\mathbf{800}\mathbf{}\mathit{R}\mathit{e}\mathit{a}\mathit{l}\end{array}$

$\begin{array}{rcl}\mathit{Y}\mathit{e}\mathit{a}\mathit{r}\mathbf{-}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{h}\mathit{o}\mathit{l}\mathit{d}\mathit{i}\mathit{n}\mathit{g}& \mathbf{=}& \mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{d}\mathit{e}\mathit{p}\mathit{o}\mathit{s}\mathit{i}\mathit{t}\mathbf{}\mathit{a}\mathit{t}\mathbf{}\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathbf{-}\mathit{e}\mathit{n}\mathit{d}\mathbf{\times }\mathit{Y}\mathit{e}\mathit{a}\mathit{r}\mathbf{-}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\\ & \mathbf{=}& \mathbf{268}\mathbf{,}\mathbf{800}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{538}\\ & \mathbf{=}& \mathbf{\$}\mathbf{144}\mathbf{,}\mathbf{614}\end{array}$