Answer:
$568.148
Step-by-step explanation:
We will relate the loan (X) with their nominal annual rate converted semiannually:
Jennifer's loan, [tex]X = 800(1+{\frac{j}{2}})^{-10*2}[/tex]
Brian's loan, [tex]X = 1,120(1+{\frac{2j}{2}})^{-10*2}[/tex]
Since Brain and Jennifer took the same amount loan, the two equations of semi annual rates can be combined thus:
[tex]X = 800(1+{\frac{j}{2}})^{-20}} = 1,120(1+{\frac{2j}{2}})^{-20}\\= {\frac{800}{1,120}}(1+{\frac{j}{2}})=(1+{\frac{2j}{2}})[/tex]
For simplicity, we will use "Y" to represent 0.714 (i.e: [tex]{\frac{800}{1,120}} = 0.714[/tex] )
Therefore, continuing with the equation above:
[tex]Y + {\frac{Yj}{2}}=1+j\\2Y+Yj=2+2j\\2Y+Yj-2j=2\\Yj-2j=2-2Y\\j(Y-2)=2-2Y\\j={\frac{2-2Y}{Y-2}}[/tex]
substituting the real value of Y (0.714) into the equation, we have:
[tex]j = {\frac{2-(2*0.714)}{0.714-2}}\\={\frac{2-1.428}{-1.286}}\\={\frac{0.572}{-1.286}}\\ =-0.445[/tex]
Solving for the value of X using j, we have:
[tex]X(1+{\frac{j}{2}})=800\\X=568.148[/tex]
