Chapter 6.4, Problem 1P

Solve each word problem

You have $6000 to invest in two stock funds. The first fund pays $5\%$ annual interest and the second account pays $9\%$ annual interest. If after a year you have made $380 in interest, how much money did you invest in each account?

To determine

To calculate: Money invested in each account .

Answer to Problem 1P

Money invest in first stock fund=$4000 and

Money invest in second stock fund=$2000.

Explanation of Solution

Given information:

Money invested in two stock: $6000.

Rate of Interest for first fund = 5%.

Rate of interest for second fund = 9%.

Interest in a year = $380.

Calculation:

Let us consider,

X be the first fund invest, therefore

  $6000-x$ will be the second fund invest.

Total interest in a year=$380

According to question,

  $\begin{array}{l}\frac{5}{100}x+\frac{9}{100}(6000-x)=380\\ 0.05x+.09(6000-x)=380\\ 0.05x+540-0.09x=380\\ -0.04x=380-540\\ -0.04x=-160\\ x=\frac{-160}{-0.04}\\ x=\$4000.\end{array}$

Now, at 5% interest we get-

  $\$4000\times \frac{5}{100}=\$200,$ and

  $6000-x=6000-4000=\$2000$

Now, at 9% interest we get-

  $\$2000\times \frac{9}{100}=\$180.$

So, Money invest in first stock fund=$4000 and

Money invest in second stock fund=$2000.