Given rate is = 7% or 0.07
Total amount needed = $12000
Time = 4 years
Here, the deposit is compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.
The equation becomes:
P= [tex]\frac{12000}{(1+\frac{0.07}{2})^{2.4}}[/tex]
P = [tex]\frac{12000}{1.035^{8}}[/tex]
Solving it, we get P = $ 9112.93
Hence $9112.93 should be deposited today.
