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
