Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.