Assume that Peter will invest $x
Then he will invest 1/2 x with a rate of 6% and 1/2 x with a rate of 14%
Since the rule of the interest is
[tex]I=\text{PRT}[/tex]
P is the amount of investment
R is the rate in decimal
T is the time
For the first account
[tex]\begin{gathered} P=\frac{1}{2}x \\ R=\frac{6}{100}=0.06 \\ T=1 \end{gathered}[/tex]
For the second account
[tex]\begin{gathered} P=\frac{1}{2}x \\ R=\frac{14}{100}=0.14 \\ T=1 \end{gathered}[/tex]
Then the interest of each account is
[tex]\begin{gathered} I_1=(\frac{1}{2}x)(0.06)(1) \\ I_1=0.03x \end{gathered}[/tex][tex]\begin{gathered} I_2=(\frac{1}{2}x)(0.14)(1) \\ I_2=0.07x \end{gathered}[/tex]
Since the total interest is $500, then add I1 and I2, equate the sum by 500
[tex]\begin{gathered} I_1+I_2=500 \\ 0.03x+0.07x=500 \\ 0.10x=500 \end{gathered}[/tex]
Divide each side by 0.10
[tex]\begin{gathered} \frac{0.10x}{0.10}=\frac{500}{0.10} \\ x=5000 \end{gathered}[/tex]
Then he invested in each account 5000/2 = $2500
He invested a total of $5000
