Answer:
He should place $26,500 in stocks and $15,900 in bonds to earn a profit of $1,696 annually
Step-by-step explanation:
In this question, we are asked to calculate the amount of principal that should be placed in two type of investments from an inheritance, to earn a particular amount of money annually.
Since we do not know these amounts, we represent them with variables. Let the amount to be invested in stocks be x and the amount to be invested in bonds be y.
Since they both total $42,400, that means we have our first equation;
x + y = $42,400 •••••••••••(I)
Now let’s calculate the profit that would be made annually on both ends;
For stocks; 2.8% annually means; 0.028x profit
For bonds; 6% annually means 0.06y
Adding both gives a profit of $1696
Mathematically;
0.028x + 0.06y = 1696 •••••••••(ii)
From the 1st equation, we can say that y = 42,400 - x
Let’s input this into the second equation;
0.028x + 0.06(42,400-x) = 1696
0.028x + 2,544 - 0.06x = 1696
0.032x = 848
x = 848/0.032 = $26,500
Recall ; y = 42,400 - x = 42,400 - 26,500 = $15,900
