Mortgages to 40 years
It knows what is the TAE
TAE are the abbreviations corresponding to Equivalent Annual Rate or Effective Annual Rate. One is an indicator that expresses in the form of percentage the yield or the costs of a certain financial product. The TAE accompanies to the nominal interest in the plans of saving, as well as in the hypothecating and personal loans. It is easier to include/understand the TAE, in saving products.
If our bank offers a plan to us of consisting of saving investing 1000 Euros to a term of a year to a nominal interest of 5%, when the year finishes, our 1000 Euros will have produced us at the end of the year an interest of, 50 Euros, that is to say 5 Euros by each 100 Euros that we had invested. But that is what it happens if instead of to give us the interests at the end of the year, give it to us in different payments throughout the year, for example monthly, and that money is united to the initial capital to secure more interests? Since that money that is united to that already we have, it also creates his interest and that it will cause that the TAE differs from the nominal interest being greater than this.
It formulates it of the TAE is the following one:
TAE = (1 + i/k) ^k 1
i is the type of annual nominal interest and k the number of payments that take place in the year.
The TAE in saving products
If we deposited to a year 1000 Euros with a nominal interest of 7%, at the end of the year, we will perceive 70 Euros of interests, that is to say, a total of 1,070 Euros, and the TAE will agree with the nominal interest, that is to say TAE = 7%. We are speaking of simple interest because the produced interests, throughout the time that extends to the deposit or plan of saving solely are produced by the initial capital. But, if hubieramos perceived the interests that the capital generates in monthly payments, we will not have received in the end a 7% of interest, but more, because the interests received in each monthly payment, have been united to the previous capital, thus generating more interests, when increasing the capital, reason why in the end, the generated interests will not be of 7%, as it says the nominal interest, but a percentage superior that will be the TAE. Now we are speaking of compound interest, because to the capital the produced interests are added to him or added periodically. When every period of payment finishes, the capital that is had is the previous capital plus the interests produced by that capital during that period. Thus if we have two possibilities of plans of saving with a same nominal interest and a same term, he is more profitable the one than more periods of payment it offers, because for every period capital is added (produced of the interests produced in that period), to the previous capital. In this case, if we deposited to the term of a year 1000 Euros with a nominal interest of 7%, and 12 payments to the year of the corresponding interests, which will be the secured final money? What TAE will have been applied?
Applying the formula we have:
TAE = (1+ 0.07/12) ^12 - 1 = 0.0723, that is to say, one TAE of 7.23%, whereas the nominal interest was of 7%.
I = (1000 * 7.23 *12)/1200 = 72.3 of interests.
1000 + 72.3 = 1072, 3 Euros, of capital in the end.
The TAE in hypothecating or personal loans
When we spoke of hypothecating or personal loans, the TAE locks up in himself much information, since it includes to the nominal interest, the expenses and banking commissions and the term of the operation, on the other hand are not including other expenses in the TAE. The expenses of appraisal of the house or the insurances are not included for example that are required by the financial organization.
If we have doubts that loan to sign between two or several, the TAE is the indicator that will help us, because for loans with different types of interest and commissions it homogenizes them to the TAE turning them to a common annual equivalent. Of all ways, also we will have to be pending of other considerations that the TAE does not pick up, like is the possibility that a financial loan can be cancelled early or of the confidence that we have with the financial organization. Also it is important that the monthly payment we consider to pay it suitable to our financial possibilities to be able to confront it with comfort. On the other hand we do not have to compare the TAE of a hypothecating loan to fixed interest with another one to variable interest, since this last one will depend much on the variation that undergoes the reference index that is applied. If both hypothecating loans are to fixed interest, if that will be very useful the TAE, because the reduced TAE more will be the one than it takes to pay less interests to us, and finally it is not either necessary to compare the TAE of a personal loan, with a hypothecating loan, since this one last one, as we commented previously are many expenses that are not included in the TAE.