Chapter 7.3, Problem 61E

To determine

The borrowed rate for Small Corporation.

Answer to Problem 61E

  $8\%:\$300,000\text{ , 9\%:\$400,000 , 10\%:\$75,000 }$

Explanation of Solution

Given information:

A small corporation borrowed $\$775,000$ to expand its clothing line. Some of the money was borrowed at $8\%$ , some at $9\%$ , and some at $10\%$ . How much was borrowed at each rate when the annual interest owed was $\$67,500$ and the amount borrowed at $8\%$ was four times the amount borrowed at $10\%?$

Calculation:

Let $a=$ amount borrowed at $8\%$

Let $b=$ amount borrowed at $9\%$

Let $c=$ amount borrowed at $10\%$

The equations are:

  $\begin{array}{l}a+b+c=775000\\ a=4c\\ 0.08a+0.09b+0.10c=67500\\ 8a+9b+10c=6750000\end{array}$

Bu using equation two, substitute for $a$ in equation first and third:

  $\begin{array}{l}(4c)+b+c=775000\\ b+5c=775000\\ 8(4c)+9b+10c=6750000\\ 9b+42c=6750000\end{array}$

Solve equation first for $b$ , substitute into equation third:

  $\begin{array}{l}b+5c=775000\\ b=775000-5c\\ 9(775000-5c)+42c=6750000\\ 6975000-3c=6750000\\ -3c=-225000\\ c=75000\end{array}$

Now, substitute the value to get the value of $a$ and $b$ :

  $\begin{array}{l}b=775000-5c=775000-5(75000)=400000\\ a=4a=4(75000)=300000\end{array}$

Thus, the borrowed rate for $8\%:\$300,000\text{ , 9\%:\$400,000 , 10\%:\$75,000 }$ .