$8,000 to invest, and hopes to earn $330 in interest in the first year.

Question

Julie has $8,000 to invest, and hopes to earn $330 in interest in the first year. She wants her investment in treasury bills to be $3000 less than her investment into corporate bonds. The expected returns (in simple interest) on each investment are: Treasury Bills: 3% Treasury Bonds: 2% Corporate Bonds: 5% How much should she invest into each one?

Answer 1

T= Treasury Bills

B=Treasury Bonds

C=Corporate Bonds

T + B + C = 8 (using units of a thousand)

T = C-3 bills are 3,000 less than corporate bonds

.03T + .02B + .05C = .33 Multiply by 100

3T + 2B +5C = 33

biggest interest is 5% with corporate bonds

8,000 invested all in corporate bonds = $400 interest

$330 is fairly close to that. Most of the investment will

be in corporate bonds

2T + 2B + 2C = 16 subtract to get

T + 3C = 17 substitute to get an equation with just one variable

C-3 + 3C = 17

C = 20/4= $5000 in corporate bonds

T = C-3 = $2000 in Treasury Bills

B = 8-T-C = 8-5-2 = $1000 in Treasury Bonds

3% of $2000 = $60

2% of $1000 = $20

5% of $5000 = $250

60+20+250 = $330

interest sums to $330

Answer 2