Base Index and Rounding Order Theory Philip J Nestingen Executive Vice President, MACC-TRAC The order of rounding and the use of a base index are two issue often misperceived in the calculation of a mortgage. Many notes, utilize a base index rate calculation as an alternative to a margin calculation or the loan may require that the index is rounded and then the margin is added to the result. Both of these special loan features poise specific needs and calculation knowledge. There is an important distinction between each of these and the common method employee in loan calculation. A Note that require a base rate calculation, typically requires the servicer to determine the change between the Base Index figure and the Current Index figure to arrive at each interest adjustment. The intent being to insure that the future interest rates will parallel the difference between the base (initial) index and the initial interest rate. Therefore, if the base (initial) index is 9% and the initial interest rate is 11% the Note intends for there to be a hypothetical margin of 2%. Many servicers will service this type of Note by subtracting the base index from the initial interest rate to arrive at a margin. With this margin the loan will be serviced similar to a loan that does not include a base index. This loan will be serviced correctly provided that the rounding is to the nearest and the initial rate is evenly divisible by the rounding factor (1/8, 1/4). However, if rounding is up or down, or if the initial interest rate is not divisible by the rounding factor, simply using a margin will not produce correct interest rates. The Base Rate Notes state that the servicer is to ‘determine the change between the Base Index figure and the Current Index figure. If the amount of change is one-eighth of one percentage point or more, the Note Holder will round the amount of change to the nearest one-eighth of one percentage point.’ The Note states the amount of change is rounded, not the result of the index plus margin. Therefore if the index is not an even eighth, the final interest rate would not be an eighth. For example if the initial rate is 10.2%, and the rounded change between the base index and the current index is 1.25, the resulting interest rate would be 11.45%. The Base Rate Note states ‘If the current Index figure is larger than the Base Index figure, the Note holder will add the rounded amount of the change to the Initial Interest Rate. If the Current Index figure is smaller than the Base Index figure, the Note Holder will subtract the rounded amount of the change from the Initial Interest Rate. The result of this addition or subtraction will be the preliminary rate.’ If the rounding method is up or down to the nearest 1/8th the calculation of the margin will not produce the correct result. Observe the following example. Initial interest rate 10.5% Base index 8.12% Hypothetical Margin 2.38% Current index value 5.38% Rounding Up to the Nearest 1/8% Method 1: (Incorrect Method) By using the method where a margin is calculated 10.5 - 8.12 = 2.38% margin Therefore the new interest rate would be 5.38 + 2.38 = 7.76% rounded = 7.875%. Method 2: (Correct Method) However by determining the change of the current index from the base index 8.12 - 5.38 = 2.74 rounded = 2.75. Subtract 2.75 from the initial interest rate of 10.5 = 7.75%. The new interest rate is 7.75%. A difference of 0.125% from Method One The reason for the difference is that in the first example where the interest rate is being rounded, the rounding up takes place after the index and margin have been added. In the second example the difference is being rounded up which results in a larger number. This difference is then subtracted from the initial interest rate. In essence the interest rate is made smaller by the rounding up method. This error will take place in all instances where the current index value is less than the base index. If a base index is input into the base index field in the rates dialog box, Vision will use the base index to determine all future interest rate adjustments. It is important to carefully read the Note when utilizing a base index. Some Notes will state a base index and a margin, but will specify that the margin be used for all future interest rate calculations. Notes that require the rounding of the index and then the addition of the margin encounter the same complications as the base index issue. If a loan is incorrectly calculate it can lead to as much as 1/8th of a percent error in a single adjustment. An error evolves from the same type of scenario as the base index issue. If rounding up takes place after the index and margins have been added, the result could be a full 1/8 of a percentage larger then if the index was first rounded and than the margin is add to the result. It is obvious the details of the method applied in calculating a loan must strictly adhere to the note documentation. Philip Nestingen can be contacted at (800) 444-7071 or  Feedback