Respuesta :
The simple interest per year is given by the following formula:
[tex]A=p(1+rt)[/tex]Where:
P= initial amount
r= rate
t= time
[tex]A=p+prt[/tex]Where: prt is the annual interest.
Therefore:
[tex]\begin{gathered} Interest4=prt=p_1*(0.04)(1) \\ Interest9=prt=p_2*(0.09)(1) \end{gathered}[/tex]We know that:
[tex]Interest4+Interest9=p_1(0.04)+p_2(0.09)[/tex]Also:
[tex]Interest4+Interest9=1,130[/tex]Replacing:
[tex]1,130=p_1(0.04)+p_2(0,095)\text{ \lparen1\rparen}[/tex]Secondly:
[tex]p_1+p_2=20,000\text{ \lparen2\rparen}[/tex]Isolating P1 in (2):
[tex]p_1=20,000-p_2\text{ \lparen3\rparen}[/tex]Substituing (3) in (1):
[tex]\begin{gathered} 1,130=(20,000-p_2)*(0.04)+p_2(0.095) \\ 1,130=800-0.04p_2+0.095p_2 \\ 1,130-800=0.055p_2 \\ 0.055p_2=330 \\ p_2=\frac{330}{0.055}=6,000 \end{gathered}[/tex]Finally, puttin P2=6,000 in equation (3):
[tex]\begin{gathered} p_1=20,000-p_2 \\ p_1=20,000-6,000=14,000 \end{gathered}[/tex]Answer: The amount she invest at each rate is $14,00 at 4% and $6,000 at 9.5%.
