Chapter 7, Problem 19CT

To determine

To find: the investment for each rate.

Answer to Problem 19CT

For 4% interest amount invested is $24000 and for 5.5% interest the amount is $26000.

Explanation of Solution

Given information:

A total $50000 is invested in two funds that pay 4% and 5.5% simple interest. The yearly interest is $2390.

Calculation:

Consider that $x$ be the amount of investment that gives 4% yearly interest and $y$ be the amount of investment that gives 5.5% interest.

The system of equation can be written as:

  $\begin{array}{c}x+y=50000\\ 0.04x+0.055y=239000\end{array}$

Multiplying the second equation throughout by 100 we get the equations as:

  $\begin{array}{l}x+y=\mathrm{500000..............}(1)\\ 4x+5.5y=\mathrm{239000.......}(2)\end{array}$

Multiplying equation (1) with -4 and adding with equation (2),

  $\begin{array}{c}-4x-4y=-200000\\ 4x+5.5y=239000\\ 1.5y=39000\end{array}$

  $y=26000$ solve for $y$

From equation (1) it is clear that $x=24000$ .

The amount invested are:

For 4% interest amount invested is $24000 and for 5.5% interest the amount is $26000.