A company placed $1,000,000 in three different accounts. It placed part in short term notes paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in utility bonds paying 4%. The income after one year was $45,500. What are the three equations needed to set this problem up? How much did the company place in each account?

Question

A company placed $1,000,000 in three different accounts. It placed part in short term notes paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in utility bonds paying 4%. The income after one year was $45,500. What are the three equations needed to set this problem up? How much did the company place in each account?

Answer 1

amount in at 4.5% --- x

amount in at 5% ----- 2x
amount in at 4% --- 1000000-3x

solve for x:

.045x + .05(2x) + .04(1000000-3x) = 45500

Answer 2

To set up this problem, we need to establish three equations based on the given information.

Let's assume the amount placed in short-term notes is x.

According to the problem statement, "twice as much" money was placed in government bonds, so the amount placed in government bonds would be 2x.

The rest of the money was placed in utility bonds, so the amount placed in utility bonds would be (1,000,000 - x - 2x) or (1 - 3x) million dollars.

Now, we can set up the equations:

1. Income from short-term notes (interest rate of 4.5%): x * 0.045
2. Income from government bonds (interest rate of 5%): (2x) * 0.05
3. Income from utility bonds (interest rate of 4%): (1 - 3x) * 0.04

The sum of these incomes should equal the total income after one year, which is $45,500:

x * 0.045 + (2x) * 0.05 + (1 - 3x) * 0.04 = 45,500

Now, we can solve this equation to find the value of x. Once we have the value of x, we can substitute it back into the equations to determine the amounts placed in each account.