At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
