Respuesta :
Answer:
• 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
Explanation:
Bank (5%)
[tex]\begin{gathered} \text{Let the amount placed at }5\%=x \\ Interest=0.05x \end{gathered}[/tex]Bonds (6%)
1/3 the amount placed in the bank was used to buy bonds
[tex]\begin{gathered} T\text{he amount used to buy bond at }6\%=\frac{x}{3} \\ \text{Interest after 1 year=}0.06\times\frac{x}{3} \\ =\frac{x}{50} \end{gathered}[/tex]Certificate of Deposit (8%)
If the total of the investments is $10,000, the balance of the funds will be:
[tex]\begin{gathered} \text{Balance}=10,000-x-\frac{x}{3} \\ =10000-\frac{4}{3}x \\ \text{Interest after 1 year}=0.08(10000-\frac{4}{3}x) \\ =800-\frac{8}{75}x \end{gathered}[/tex][tex]undefined[/tex]The first year, the investments bring a return of $745. Therefore, we sum up all the interests:
[tex]\begin{gathered} 0.05x+\frac{x}{50}+800-\frac{8}{75}x=745 \\ \frac{5}{100}x+\frac{1}{50}x-\frac{8}{75}x=745-800 \\ (\frac{5}{100}+\frac{1}{50}-\frac{8}{75})x=745-800 \\ -\frac{11}{300}x=-55 \\ x=55\times\frac{300}{11} \\ x=1500 \end{gathered}[/tex]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
