Question

What is the present value of $100 to be deposited today into an account paying 8.0%, compounded semi-annually for two years?

Answer 1

Giving the following information:

Initial Investment (PV)= $100

Number of periods (n)= 4 semesters

Interest rate (i)= 0.08/2 = 0.04 compounded semiannually

The investment varies with the interest earned over time. Therefore, the present value of the investment is $100. No time has passed.

Now, if we want to calculate the future value two years from now, we need to use the following formula:

FV = PV*(1 + i)^n

Replacing,

FV= 100*(1.04^4)

FV= $116.99

Answer 2

The Answer is that the present value of $100 is $100.
Because this $100 dollar is deposited today so the time is equal to zero and when time is zero the value of amount is the value of amount itself.
As the account is paying 8% compounded semi annually for two years but that does not have any effect on the $100 you are depositing today.
If the question is in such a way that they asked for the present value of $100 that was deposited two years ago than we calculate.