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Say you borrow $1000 for one year at a flat rate of12%. 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 is16% rather than the12% 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 annualized interest rate of24% 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.
Another way (and probably simpler) to explain effective interest is to consider each of the four individual payements. Payment1 - $30 interest is12% of the principal payment of $250. But this principal component has only been borrowed for3 months. Effectively, the annualised interest paid on this component is48% Payment2 - $30 interest is12% of the principal payment of $250. But this principal component has only been borrowed for6 months. Effectively, the annualised interest paid on this component is24% Payment3 - $30 interest is12% of the principal payment of $250. But this principal component has only been borrowed for9 months. Effectively, the annualised interest paid on this Payment4 - $30 interest is12% of this final principal payment of $250. This is the only principal component that has been borrowed for the whole12 months. Effectively, the entire loan has had an interest charge of about twice the flat interest rate for the whole year. This rate is called the effective rate and, in further maths, is found by (2n)/n+1) times the flat rate. In this example, it is about22.15%
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.
Say you borrow $1000 for one year and you will repay this loan plus interest in monthly payments, eatch payment $100.
the flat rate is20%
the effective rate is21.939%
flat rate interest - same interest rate is fixed through out the period for the total loan
effective interest rate - same interest rate is fixed through out the period for a loan which will be diminising
Flat Interest rate is a fixed rate which is offerred by most of the banks through competition, while effective interest rate is calcluated as follows:
1- Rate on Risk free securities +
2- Inflation rate +
3- Economic Risk
The flat Interest rate/Simple Interest rate is what you see now, like3.5% for the5 to7 years loan.which mean3.5% flat interest rate on your principal loan through out the next5 to7 years.This is easily to calculate.
So, Effective interest rate is derived from the flat interest rate.It is the rate of interest for the period of period t to t+1 formula.
Flat Interest formula
Interest = PRINCIPLE X Interest rate X TIME
time for the whole period
Effective Annual I = (1+ I/M)^m
Reduce interest = Principle BalanceX interest rate X time
time for the period till balance change