7. find the present value. amount needed: $42,000 time (years): 8 rate: 3% compounded: semiannually $37,283.82 $36,960.00 $33,097.26 $33,155.22

To solve this we are going to use the formula for a future value: 
where
is the future value 
is the present value 
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the time in years

Since the amount needed is $42,000, . We also know for our problem that  and . Since the interest is compounded semiannually, it is compounded two times per year; therefore, . Lets replace those values in our formula and solve for :





We can conclude that the present value needed to make $42000 after 8 years according to your given choices is $33,097.26