Question

Kelly has $20000 to invest, and hopes to earn $1390 in interest in the first year. She wants her investment in treasury bills to be $3000 more than her investment in corporate bonds. The expected return (in simple interest) on each investment are: Treasury Bills: 5%, Treasury Bonds: 7%, Corporate Bonds: 10%. How much should Kelly invest in each one?

Answer 1

Answer:

$8,000 in Treasury bills

$7,000 in Treasury bonds

$5,000 in corporate bonds

Step-by-step explanation:

Let the amount to be invested in treasury bills be $x , the amount to be invested in treasury bonds be $y

From the question, we understand that the amount she will invest in corporate bonds will be $3000 less than the amount in treasury bills;

So mathematically, this will be $(x - 3000)

So therefore, the amount invested in each will be;

x + y + x-3000 = 20,000

2x + y = 20,000 + 3000

2x + y = 23,000 ••••••••(i)

Let’s now work with the simple interests;

For treasury bills;

5% = 5/100 * x = 5x/100

For Corporate bonds ;

10% = 10/100 * (x -3000) = (x-3000)/10

For Treasury bonds 7%

7% = 7/100 * y = 7y/100

Adding all gives the total interest;

5x/100 + 7y/100 + (x-3000)/10 = 1390

Multiply through by 100

5x + 7y + 10(x-3000) = 1390 * 100

5x + 7y + 10(x-3000) = 139,000

5x + 7y + 10x -30,000 = 139,000

15x + 7y = 139,000 + 30,000

15x + 7y = 169,000 •••••••••(ii)

So we have two equations to solve simultaneously;

From i, y = 23,000 - 2x

Put this into ii

15x + 7(23,000 -2x) = 169,000

15x + 161,000 - 14x = 169,000

x + 161,000 = 169,000

x = 169,000 - 161,000

x = $8,000

y = 23,000 - 2x

y = 23,000 - 2(8,000)

= 23,000 - 16,000 = $7,000

So the last investment amount is x-3000 = 8,000 -3,000 = $5,000