# Thread: difference between flat rate and effective interest rate ?

1. ## difference between flat rate and effective interest rate ?

hey guys

i've read this over and over in the maths textbook but i cant get a grasp on the difference between the 2

can someone explain to me why there is such a large difference between the 2?

thanks

2. ## Re: difference between flat rate and effective interest rate ?

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.

3. ## Re: difference between flat rate and effective interest rate ?

Another way (and probably simpler) to explain effective interest is to consider each of the four individual payements.
Payment 1 - \$30 interest is 12% of the principal payment of \$250. But this principal component has only been borrowed for 3 months. Effectively, the annualised interest paid on this component is 48%
Payment 2 - \$30 interest is 12% of the principal payment of \$250. But this principal component has only been borrowed for 6 months. Effectively, the annualised interest paid on this component is 24%
Payment 3 - \$30 interest is 12% of the principal payment of \$250. But this principal component has only been borrowed for 9 months. Effectively, the annualised interest paid on this
Payment 4 - \$30 interest is 12% of this final principal payment of \$250. This is the only principal component that has been borrowed for the whole 12 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 about 22.15%

4. ## Re: difference between flat rate and effective interest rate ?

thanks a lot, that's helped me a lot!!

have a sweet holiday

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