A person invests $500 in an account that earns a nominal yearly interest rate of 4%.

a. if the interest rate is 4% , the account will grow 4% more than the year before  EACH YEAR   

     initial 500 deposit will be worth   500 x 1.04 at the end of year 1 = $520

     at the end of the SECOND year, due to compounding, it will be worth   520 x 1.04=$ 540.80

   after 10 years    the formula becomes    500 (1.04)^10 = $ 740.12

b.1.04 is the interst applied PER YEAR     .... now the compounding period is 3 months....4 PERIODS per year..

..the periodic interest is then  .04/4 = .01/period    for 40 periods (10 years)

     and the formula becomes    

        500 (1.01)^40 = 744.43      NOTE: Due to COMPOUNDING this works out to be GREATER than 4% per year

                                                      (perhaps you have heard "APR"   = annual percentage rate     or

                                                              APY = annual percentage yield)

c. 1.04  = (1+x)^4      x = .009853  or 0..09853 %  per quarter compounding

d.  500 (1+ .009853)^40 = 740.12

You are welcome....this stuff will be very important to you later in your financial life (REALLY!)....learn it well!  ~EP