Respuesta :
Let, x be the amount she invest in the bond which pays 15% of interest.
Then, $70000-x would be the amount she would be investing in a CD that pays 7% of interest.
We know the simple interest formula is: [tex]\\ I=\frac{P\times R\times T}{100}[/tex]
Case I: Let [tex]I_{1}[/tex] be the interest she gets on investing $x amount in bond which gives 15% of interest.
Thus, [tex]P_{1}=x, R_{1} =15\%, T_{1} =1[/tex]
Hence we have now,
[tex]\\ I=\frac{x\times 15\times 1}{100}\\ =\frac{15x}{100}[/tex]
Case II: Let [tex]I_{2}[/tex] be the interest she gets on investing $(70000-x) amount in CD which gives 7% of interest.
Thus, [tex]P_{2}=70000-x, R_{2} =7\%, T_{2} =1[/tex]
Hence we have now,
[tex]\\ I_{2}=\frac{(70000-x)\times 7\times 1}{100}\\ \\ =\frac{490000-7x}{100}[/tex]
Since, the woman needs to make a total interest of $9000 each year,
[tex]\\ I=I_{1}+I_{2}\\ \Rightarrow 9000=\frac{15x}{100}+\frac{490000-7x}{100}\\ 900000=15x-7x+490000=8x+490000\\ 410000=8x\\ x=\frac{410000}{8}=51250[/tex]
⇒The amount she invest in bond = x= $51,250
Thus, the amount she invest in CD = $70,000 - x= $70,000 - $51,250= $18,750
Therefore, the amount that women should invest in bond is $51,250 and in CD is $18,750 so that she can get a total interest of $9000 every year.
