Paul has $60,000 to invest. His intent is to earn 14% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest. How much does Paul need to invest in each option to make a total 14% return on his $60,000?
Well, Paul is in quite a pickle! Splitting his investment between two options with different interest rates can be tricky, but fear not, I am here to help. Let's break it down!
Let's say Paul invests x amount of dollars at 8% interest. That means he would invest (60000 - x) at 16% interest.
To calculate Paul's annual return, we multiply the amount invested at each interest rate by the respective interest rate, and sum those up. Then we divide the total annual return by the total investment amount:
(0.08 * x + 0.16 * (60000 - x)) / 60000 = 0.14
Now, let's solve this equation:
0.08x + 0.16(60000 - x) = 0.14(60000)
0.08x + 9600 - 0.16x = 8400
-0.08x = -1200
x = 15000
So, Paul needs to invest $15,000 at 8% interest and the remaining amount, $45,000, at 16% interest to make a total 14% return on his $60,000 investment.
To solve this problem, we can set up a system of equations.
Let's say Paul invests x dollars at 8% interest and y dollars at 16% interest. The total amount of money Paul invests is $60,000, so we have the equation:
x + y = 60,000 -------(equation 1)
Paul's goal is to earn a total return of 14%. We can express this as a decimal and multiply it by his total investment to find the total return. The equation for the total return is:
0.14 * 60,000 = 0.08x + 0.16y -------(equation 2)
Now we have a system of equations:
x + y = 60,000 -------(equation 1)
0.08x + 0.16y = 0.14 * 60,000 -------(equation 2)
To solve the system, we can use substitution or elimination method. Here, we'll use substitution:
From equation 1, we have x = 60,000 - y.
Substituting this into equation 2, we get:
0.08(60,000 - y) + 0.16y = 0.14 * 60,000
4,800 - 0.08y + 0.16y = 8,400
0.08y = 3,600
y = 3,600 / 0.08
y = 45,000
Now, substitute this value of y back into equation 1 to find x:
x + 45,000 = 60,000
x = 60,000 - 45,000
x = 15,000
So, Paul needs to invest $15,000 at 8% interest and $45,000 at 16% interest to make a total 14% return on his $60,000.
To find out how much Paul needs to invest in each option, we can use a system of equations.
Let's assume Paul invests an amount x at 8% interest, and (60000 - x) at 16% interest.
The interest earned on the investment at 8% would be 0.08x, and the interest earned on the investment at 16% would be 0.16(60000 - x).
Since Paul wants to earn a total of 14% interest on his $60,000 investment, we can set up the equation:
0.08x + 0.16(60000 - x) = 0.14(60000)
Simplifying the equation, we get:
0.08x + 9600 - 0.16x = 8400
Combine like terms:
-0.08x + 9600 = 8400
Subtract 9600 from both sides:
-0.08x = -1200
Divide by -0.08 to solve for x:
x = -1200 / -0.08
x = 15000
Therefore, Paul needs to invest $15,000 at 8% interest and $45,000 (60000 - 15000) at 16% interest to make a total 14% return on his $60,000.
add up the interests:
8x + 16(60000-x) = 14*60000