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
Answers
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
Solution :-
Let us assume that, the company placed $x into short term notes .
so,
→ $x at 5.5% per year.
→ $3x at 5% per year .
→ $(500000 - 4x) at 4.5% per year .
A/q,
→ Total income in 1 year = $25000
→ (x * 5.5/100) + (3x * 5/100) + (500000 - 4x)4.5/100 = 25000
→ (5.5x + 15x + 2250000 - 18x) = 25000 * 100
→ 20.5x - 18x = 2500000 - 2250000
→ 2.5x = 250000
→ x = $100000
therefore,
→ Company placed in government bonds = $3x = 3 * 100000 = $300000
and,
→ Company placed in utility bonds = (500000 - 4x) = 500000 - 400000 = $100000
hence,
→ More money did the company place in government bonds than in utility bonds = 300000 - 100000 = $200000 (B) (Ans.)
Learn more :-
Sahil deposited an amount in a bank at a certain rate of interest which is compounded annually. When he
inquired from th...
https://brainly.in/question/26967119
If there is 45% increase in amount in 3 years at simple interest, what will be the compound interest of Rs.
12,000 at th...
https://brainly.in/question/26772982