Question

In Problem 18, what long-term interest rate would represent a break-even point between using short-term financing as described in part a and long-term financing? (Hint: Divide the interest payments in 18a by the amount of total funds provided for the six months and multiply by 12.)

Short answer

The monthly interest rate will be 1.014%, and 12.17% will be the annual interest rate.

Step-by-step solution

Interest payments

January	$8,500
February	$2,500
March	$3,500
April	$8,500
May	$9,500
June	$4,500

Calculation of break-even point

The break-even point will be 1.014% monthly rate and 12.17% annual rate.

$\begin{array}{rcl}\mathit{B}\mathit{r}\mathit{e}\mathit{a}\mathit{k}\mathbf{-}\mathit{e}\mathit{v}\mathit{e}\mathit{n}\mathbf{}\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}& \mathbf{=}& \frac{\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}}{\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{i}\mathbf{p}\mathbf{l}\mathbf{e}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{373}\mathbf{.}\mathbf{35}}{\mathbf{\$}\mathbf{37}\mathbf{,}\mathbf{000}}\\ & \mathbf{=}& \mathbf{1}\mathbf{.}\mathbf{014}\mathbf{\%}\end{array}$

$\begin{array}{rcl}\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathit{I}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{s}\mathit{t}\mathbf{}\mathit{R}\mathit{a}\mathit{t}\mathit{e}& \mathbf{=}& \mathit{M}\mathit{o}\mathit{n}\mathit{t}\mathit{h}\mathit{l}\mathit{y}\mathbf{}\mathit{i}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{s}\mathit{t}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathbf{\times }\mathbf{12}\\ & \mathbf{=}& \mathbf{1}\mathbf{.}\mathbf{014}\mathbf{\%}\mathbf{\times }\mathbf{12}\\ & \mathbf{=}& \mathbf{12}\mathbf{.}\mathbf{17}\mathbf{\%}\end{array}$