Chapter 3.5, Problem 42PPSE

Solution

Tocalculate:The amount worker placed in each account if he received a $10,000 bonus and decided to split it among three different accounts. He placed some money in savings account paying 4.5% per year, twice as much in government bonds paying 5% and the rest in a mutual fund that returned 4%. His total income after one year was $455.

He placed $2200 in savings account, $4400 in government bonds and $3400 in mutual funds.

Given information:

A Worker received a $10,000 bonus and decided to split it among three different accounts. He placed some money in savings account paying 4.5% per year, twice as much in government bonds paying 5% and the rest in a mutual fund that returned 4%. His total income after one year was $455.

Calculation:

Consider the given information.

Let theamount invested by the worker in savings account isx , amount invested in government bondsy , and amount invested in mutual funds isz .

Since the total amount is10,000 so $x+y+z=10,000$

He invested twice as much in government bonds paying 5% and the rest in a mutual fund that returned 4%.

  $y=2x$

Put $y=2x$ in $x+y+z=10,000$ .

  $\begin{array}{c}x+2x+z=10,000\\ 3x+z=10,000\\ z=10,000-3x\mathrm{...}\left(1\right)\end{array}$

Translate the given information into algebraic equation.

  $\begin{array}{c}0.045x+0.05y+0.04z=455\\ 45x+50y+40z=455,000\end{array}$

Put $y=2x$ in $45x+50y+40z=455,000$ .

  $\begin{array}{c}45x+50\left(2x\right)+40z=455,000\\ 145x+40z=455,000\end{array}$

Now use the equation 1.

  $\begin{array}{c}145x+40\left(10,000-3x\right)=455,000\\ 145x+400,000-120x=455,000\\ 25x=55,000\\ x=2200\end{array}$

Put $x=2200$ in equation 1.

  $\begin{array}{l}z=10,000-3\left(2200\right)\\ z=3400\end{array}$

Put $x=2200$ and $z=3400$ into $x+y+z=10,000$ .

  $\begin{array}{l}2200+y+3400=10,000\\ y=4400\end{array}$