Question

I have $20,000 to invest. I plan to diversify and invest in three different investments: treasurybills that yield 5% simple interest, treasure bonds that yield 7% simple interest, and corporatebonds that yield 10% simple interest. I want to earn $1390 per year in income from these

investments. I plan to make my investment in treasury bills to be $3,000 more than my investment
in corporate bonds. How much money should I place in each investment? (20 points)

Answer 1

Answers:

• treasury bills = $8000
• treasury bonds = $7000
• corporate bonds = $5000

Explanation:

Define the three variables x, y, and z.

• x = amount invested in treasury bills
• y = amount invested in treasury bonds
• z = amount invested in corporate bonds

x+y+z = 20000 is the total amount invested

0.05x+0.07y+0.10z = 1390 = desired income per year

x = z+3000 since you want $3000 more invested with treasury bills compared to corporate bonds.

The starting system of equations is

x+y+z = 20000

0.05x+0.07y+0.10z = 1390

x = z+3000

Let's replace each copy of x with z+3000 in the 1st equation

x+y+z = 20000

z+3000+y+z = 20000

y+2z = 20000-3000

y+2z = 17000

y = -2z+17000

Do the same for the 2nd equation.

0.05x+0.07y+0.10z = 1390

0.05(z+3000)+0.07y+0.10z = 1390

0.05z+150+0.07y+0.10z = 1390

0.07y+0.15z = 1390-150

0.07y+0.15z = 1240

We have this new system

y = -2z+17000

0.07y+0.15z = 1240

Let's apply substitution to solve for z.

0.07y+0.15z = 1240

0.07(-2z+17000)+0.15z = 1240

-0.14z+1190+0.15z = 1240

0.01z+1190 = 1240

0.01z = 1240-1190

0.01z = 50

z = 50/0.01

z = 5000 dollars is invested in corporate bonds.

Use this to determine the value of y

y = -2z+17000

y = -2*5000+17000

y = -10000+17000

y = 7000 dollars is invested in treasury bonds.

Use the values of y and z to determine x.

x+y+z = 20000

x+7000+5000 = 20000

x+12000 = 20000

x = 20000-12000

x = 8000 dollars invested in treasury bills.