Suppose you put $100 into a savings account today, the account pays a nominal annual rate of 6%, but compounded semiannually, and you withdraw $100 after 6 months

First We calculate the future value (FV) of $ 100 deposited over 20 years using Financial Calculator. 

Here,

N = Number of periods = 2*20 = 40 Periods

I/Y = Interest rate per period = 6%/2 = 3% compounded semiannually

PMT = Payment per period = 2

PV = Present Value = $100

FV = $326.20

Now, 

We calculate FV of $ 100 withdrawn after 6 months, over the 19.5 years:

Here,

N = Number of periods = 2*19.5 = 39 Periods

I/Y = Interest rate per period = 6%/2 = 3% compounded semiannually

PMT = Payment per period = 2

PV = Present Value = $100

FV = $316.70

So,

Ending Balance  20 years after the initial $100 deposit was made =  $326.20 - $316.70 = $9.50