Respuesta :
Hello there. To solve this question, we'll have to remember some properties about investments.
Consider this is a simple investment, such that for a principal value P invested at an interest rate r for a period of t (say, years, months, so on...), the interest earned is given by
[tex]I=P\cdot r\cdot t[/tex]This can be interpreted as the return of this investment due to the interest rate r.
Now, we want to determine a value x for which when investing this value at an interest rate of 6%, considering Ed Moura's other $72000 investment paying 9%, he has an average return of 7%.
For this, we assume that for a certain period of time t
[tex]\begin{gathered} I_1:\text{ investment in stocks given by }72000\cdot0.09\cdot t \\ I_2:\text{ investment in certificates given by }x\cdot0.06\cdot t \\ \text{total investment }=72000+x \\ \text{ Average return }=(72000+x)\cdot0.07\cdot t \\ \end{gathered}[/tex]Such that we get
[tex]\begin{gathered} Avg=\dfrac{I_1+I_2}{2} \\ \\ \Rightarrow(72000+x)\cdot0.07\cdot t=\dfrac{72000\cdot0.09\cdot\,t+x\cdot0.06\cdot\,t}{2} \\ \\ (72000+x)\cdot0.07\cdot t=36000\cdot0.09\cdot\,t+x\cdot0.03\cdot\,t \end{gathered}[/tex]Simplify the equation by a factor of t, t > 0
[tex](72,000+x)\times0.07=36,000\times0.09+x\times0.03[/tex]Expand the left hand side
