Answer:
We will consider positive interest rate which is i=0.21 or i=21%
Explanation:
The formula for Future value is:
[tex]FV=PV(1+i)^n[/tex]
The present value will become:
[tex]PV=FV(1+i)^{-n}[/tex]
where:
n is the number of years
Since the condition is same present value,so the given data form the equation:
[tex]6000+5940(1+i)^{-1}=12000(1+i)^{-1/2}[/tex]
Divide above equation by [tex](1+i)^{-1}[/tex]
[tex]6000(1+i)+5940=12000(1+i)^{1/2}[/tex]
Let [tex]z=(1+i)^{1/2}\\[/tex]. Above equation will become:
[tex]6000z^2+5940=12000z[/tex]
Rearranging above equation:
[tex]5940-12000z+6000z^2=0[/tex]
Solving the quadratic equation:
z=1.1, z=0.9
Let [tex]z=(1+i)^{1/2}\\[/tex] will become:
[tex]z=(1+i)^{1/2}\\\\z^2=1+i[/tex]
[tex]i=z^2-1[/tex]
For z=1.1
[tex]i=(1.1)^2-1\\i=0.21[/tex]
For z=0.9
[tex]i=(0.9)^2-1\\i=-0.19[/tex]
we will consider positive interest rate which is i=0.21 or i=21%
