Respuesta :
ANSWER :
$40,000 for 6% and $130,000 for 12%
EXPLANATION :
The formula for interest is :
[tex]I=P\times r\times t[/tex]Where I is the interest
r is the rate of interest
t is the time in years
Their total investment is $170,000, and they want to divide it into two parts, let's say P1 and P2.
P1 + P2 = 170,000
One investment has 6% interest, and the other has 12%.
So we have r1 = 6% or 0.06
and r2 = 12% or 0.12
Solve for the interest in t = 1 year
[tex]\begin{gathered} I_1=P_1r_1t \\ I_1=P_1(0.06)(1) \\ I_1=0.06P_1_{} \end{gathered}[/tex][tex]\begin{gathered} I_2=P_2r_2t \\ I_2=P_2(0.12)(1) \\ I_2=0.12P_2 \end{gathered}[/tex]They want to have an interest of $18,000 per year.
So I1 + I2 = 18,000
This will be :
[tex]\begin{gathered} I_1+I_2=18000 \\ 0.06P_1+0.12P_2=18000 \end{gathered}[/tex]From the first equation we have :
P1 + P2 = 170,000
Express P1 in terms of P2 :
P1 = 170,000 - P2
Substitute this P1 to the equation above.
[tex]\begin{gathered} 0.06P_1+0.12P_2=18000 \\ 0.06(170000-P_2)+0.12P_2=18000 \\ 10200-0.06P_2+0.12P_2=18000 \\ -0.06P_2+0.12P_2=18000-10200 \\ 0.06P_2=7800 \\ P_2=\frac{7800}{0.06}=130,000 \end{gathered}[/tex]Now we have P2, solve for P1
[tex]\begin{gathered} P_1=170000-P_2 \\ P_1=170000-130000 \\ P_1=40000 \end{gathered}[/tex]Therefore, the investment will be $40,000 and $130,000
