Question

Suppose you received an unexpected inheritance of $42,400. You have decided to invest the money by placing some of the money in stocks that pay 2.8% and the rest in bonds that pay 6%. How much should you place in each investment in order to earn 4%, or $1696 annually?

Answer 1

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