Say you borrow $1000 for one year at a flat rate of 12%. Let's then say you will repay this loan plus interest in four quarterly payments.
A flat rate (or simple interest) calculation says that the total interest for the year is $120. Therefore, you must repay $250 principal reduction + $30 for the interest at each repayment. At each quarter, you are paying one quarter of the total interest due for the whole year. After the first payment, you still owe $750 of the principal and $90 for the remaining interest over the remaining nine months (3 more payments) of the loan.
Just consider the calculation of a loan of $750 taken for three quarters (9 months) and the interest turns out to be $90 for this period. If you put this info into the Simple Interest formula, you will find the annual rate of interest for this loan is 16% rather than the 12% you may have expected.
Look at what happens in mid-year with the "flat rate loan". You will have $500 to pay in the remaining two payments for six months and you still owe the remaining $60 interest. In effect, you are borrowing $500 for half a year and paying interest of $60 for this. Again use the simple interest formula and you will find you would effectively be paying an annualised interest rate of 24% on this $500.
Effective interest rates take into account the fact that you are NOT borrowing the entire principal for the entire loan. Each repayment is decreasing the principal. A flat rate calculation presumes the whole principal is borrowed for the entire loan period.
Hope this helps a little.