Question

A company placed $500,000 in three different investment plans.

The company placed some money into short-term notes paying 5.5% per year. They placed three times as much into government bonds paying 5% per year. They placed the rest in utility bonds paying 4.5% per year.

The income for one year was $25,000. How much more money did the company place in government bonds than in utility bonds?

A. $100,000
B. $200,000
C. $300,000
D. $400,000

Answer 1

Answer:

B. $200,000

Step-by-step explanation:

Let x be the amount placed at 5.5%

3x is the amount placed at 5%

This leaves the rest for the 4.5 %   500000- x - 3x = 500000-4x

Assuming simple interest

I = PRT where I is interest, P is principle, rate is rate and t  is time

Interest for the 5.5% for 1 year is

I = x * .055 * 1 = .055x

Interest for the 5.% for 1 year is

I = 3x * .05 * 1 = .15x

Interest for the 4.5% for 1 year is

I = 500000-4x * .045 * 1 = 22500 - 0.18 x

Add the interest together to get the income for 1 year

.055x+  .15x+22500 - 0.18 x=25,000

Combine like terms

0.025x+22500=25000

Subtract 22500

.025x =2500

Divide by .025

x =100000  

short term notes is 100000

3*x = 300000 = government bonds

The rest is utility bonds 500000- 100000-300000 = 100000

We want how much more in government bond than utility bond

300000 -100000 = 200000

Answer 2

Answer:

200000

Step-by-step explanation:

the short term =x

government bonds =3x

utility bonds: 500000-4x

0.055x+3(0.05(x)+0.045(500000-4x)=25000

0.055x+0.15x+22500-0.18x=25000-22500

0.055x+0.15x+22500-0.18x-22500=2500

0.025x=2500

x=2500/0.25

x=100000

government bonds=3x=3(100000)=300000

utility bond=(500000-400000)=100000

government bonds than in utility bonds:

300000-100000=200000