Question

The controller (money manager) for a small company puts some money in a bank account paying 5% per year. He uses come additional money, amounting to 1/3 the amount placed in the bank, to buy bonds paying 6% per year. With the balance of the funds, he buys a 8% certificate of deposit. The first year the investments bring a return of $745. If the total of the investments is $10,000 how much is invested at each rate?

Answer 1

• The amount put in the bank = $1,500

• The amount used to buy bond = $500

,

• The amount used to buy the certificate of deposit =$8000

Step-by-step explanation:

Bank (5%)

`\begin{gathered} \text{Let the amount placed at }5\%=x \\ Interest=0.05x \end{gathered}`

Bonds (6%)

1/3 the amount placed in the bank was used to buy bonds

`\begin{gathered} T\text{he amount used to buy bond at }6\%=(x)/(3) \\ \text{Interest after 1 year=}0.06*(x)/(3) \\ =(x)/(50) \end{gathered}`

Certificate of Deposit (8%)

If the total of the investments is $10,000, the balance of the funds will be:

`\begin{gathered} \text{Balance}=10,000-x-(x)/(3) \\ =10000-(4)/(3)x \\ \text{Interest after 1 year}=0.08(10000-(4)/(3)x) \\ =800-(8)/(75)x \end{gathered}`

The first year, the investments bring a return of $745. Therefore, we sum up all the interests:

`\begin{gathered} 0.05x+(x)/(50)+800-(8)/(75)x=745 \\ (5)/(100)x+(1)/(50)x-(8)/(75)x=745-800 \\ ((5)/(100)+(1)/(50)-(8)/(75))x=745-800 \\ -(11)/(300)x=-55 \\ x=55*(300)/(11) \\ x=1500 \end{gathered}`

Thus:

• The amount put in the bank = $1,500

,

• The amount used to buy bond = 1500/3 = $500

,

• The amount used to buy certificate of deposit = 10,000-2000=$8000