Apples or pears, quota or deadline.
When I was a tadpole, my math teacher I ever had instilled add apples with pears. Apparently it is a truism almost insulting, but obviously there are many people who understood the example but not assimilated the concept. This same idea was repeated by the financial math professor several years later in college. "You can not add apples with pears like you can not add money today with tomorrow's money"
- If they offer you 50 € a month for 3 months, how you today? ¿150 €?
- What do you prefer € 100 or € 100 today morning? It seems clear that today, so are worth more today than € 100 € 100 tomorrow.
The capital can not add or compare if they are not at the same moment in time and to achieve this movement, we must apply a discount rate (the price of deferring capital at the time), which will set as our criteria, but is often used as provided you order it would cost to a bank (Euribor + differential).
So far today is worth the rent (set of payments) Example 3 payments of 50 € if the first payment is made today. Pongo as a 5% discount rate (0.42% monthly).
- The first payment today is worth 50 €
- The second payment is worth 49.79 € → today [50 / (1.0042)] (50 € a months back)
- The third payment worth € → 49.58 today [50 / (1.0042) ²] (50 € two months back)
The value today of an income of 3 monthly payments of 50 euros with payment beginning of period (prepay) is € 149.37. Apparently this is not an exorbitant difference, but the effect of time increases these differences.
If you would like to add € 50 today and 50 € in a year, would see that today are worth € 50 and € 50 within a year, worth € 47.61 today [50 / (1.05)], thus the apparent 100 € actually worth € 97.61 (today). It is also true that same income of 2 payments of 50 €, a year will be worth 102.50 € [50 +50 x1.05].
Capital to move forward and to move towards increased last fall at a rate of (1 + r) n where r is the discount rate and "n" the number of periods.
These simple examples are not intended to be a crash course in financial mathematics, tomadlo as a demonstration that you can not add apples with pears so nobody takes as an act of faith that comment on the reasoning below. The faith for religion, for everything else, facts and numbers. Until everyone here agree? Well agárrense coming curves, I return to the topic or time share?
Example, asked the typical blog:
I have a mortgage with € 150,000 outstanding and payable 25 years and I will recoup € 6,000. (Euribor + 0.50). Against quota or against term?Sample response typical blog:
With an Excel that I have that I get paid a fee of € 867.21.
If you save time to amortize 22 shares and a half or 19446.54 € (867 * 22 +499)
If amortized share pay € 832.52 which means a saving of € 34.69 x 300 shares = 10,407 €
Therefore depreciated term that leaves you 9.000 € better!
The question is recursive and cansina on the blog, but the answer is a financial disaster, adding apples, pears and kiwis and comparing it to the sum of a bunch of celery and some oranges Washington.
In the case of repayment term, these are poorly € 19,446 plus, but in what it is close in time (almost 2 years between the first and last, but we could give it to "not very wrong"), but what is serious is that no one takes into account that, on average, are within 24 years.
In case of reduction of share, are joining the € 34.69 that fail to pay today with the € 34.69 that fail to pay within 25 years at the latest installment, which capitalized as of today would have a value of 10 , 28 €.
The correct answer is:
€ 6,000 amortization term is equivalent to the value today of an income consists of a payment of 367 € within 23 years and 2 months, followed by 22 monthly payments of € 867.21, right? ... I mean, I give today 6000 € to change that within 23 years and two months I will start to Receivables (fail to pay an obligation which I have) such income.
€ 6,000 to amortize share is equivalent to a monthly rent of 34.69 € for 300 months. OK? ...
Does everyone agree? So we had to do the calculations of the present value of these revenues as of today to know that we should go out and doubts once and for all.
CALCULATIONS TERM
First take the 23 payments at the end of the month put them at 300 for a single point in time. (There is a formula, but it can be done with Excel without any problems).
367 x € 1.0040741 22 = 401.34 €
867 x € 1.0040741 21 = 944.51 €
867 x € 1.0040741 20 = 940.68 €
867 x € 1.0040741 19 = 936.86 €
... ...
867 x € 1.0040741 01 = 870.74 €
867 x € 1.0040741 00 = 867.21 €
Suman 20318.71 € and now I bring this capital 300 months back in time to meet its current value.
20318.71 / (1.004074123) 300 = € 6000.17 (what chance does not?)
CALCULATIONS TO SHARE
We estimate the current value of an income of 300 monthly payments of € 34.69
The present value of this income is 6003.27.
CONCLUSIONS:
Whatever you do, stop what you amortize duty, and the present value of what is to amortize the amount to amortize (as insulting as evident from the pears and apples huh?), Or that there is no better option worse, in any case we can say that we prefer one or the other, but that already are subjective considerations.
Financially, it can absorb an early repayment as the "barter" for a specified amount today (€ 6,000) in exchange for the saving of several amounts deferred morning in time (either € 34.69 per month for 25 years or 22 monthly payments € 867 within 23 years).
Further considerations:
- If you take another discount rate to Euribor +0.50 different, the result would be another number, but it would be the same for both share to term if the discount rate is constant. The other rate could be what the bank pays us in a warehouse, to know what more we should.
- If considerásemos that the rate could vary (which is what will happen but I guess it clear that you do not know where), then if it could be a more profitable strategy than the other, because the pay structure of the two incomes is different, occurring in an end-all, and the other occurring on a regular basis throughout the lifetime of income.
- a) In a scenario of rising rates (throughout the life of the operation) would be better to amortize share, since the amounts paid in the end, to apply a higher discount rate would have a lower current value, then the repayment to term, which gives its fruit at the end of the operation would have a present value lower.
- b) In a scenario of declining rates, we might be interested in reducing against time because the capitalization of the payments will be done away with a discount rate lower, therefore the equivalent income will be less penalized and a higher current value.
The most likely is that the variation in rates is increasing in some periods and decreasing in others (25 years to give much), so you will not get to know us better comes out until you have completed the transaction. So once again demonstrated that the economy and finances are a pseudo-science that goes very well to "predict" the past, but for the future better call the pitonisa Lola.
All this explanation seems to sink into misery Table Excel inspection family budget that he proposed two weeks ago, but despite that sum apples with pears, we can take for valid, as it is periods of less than one year, and has income and expenses, and all re reduced to update its value, so the gap caused by the effect only affects the time differential between these. (reduced revenues, but also costs are reduced by the same proportion to capitalize)
And to finish and try to deduce whether rates will rise or fall in the future, if we should save or amortization, or simply to take away some uncertainty, which better than reading the news of the day.
- The harmonized CPI down three tenths in September to 4.6%
- Congress reached final agreement on the financial rescue plan
- Belgium, Netherlands and Luxembourg injected 11,200 million euros in Fortis
- Santander will buy the branch network of Bradford & Bingley for 500 million euros
- The upswing in the Euribor rate rises to 6% mortgage half
- The Santander negotiated by the Wachovia bank, according to Wall Street Journal
- "You can not give 700,000 million to banks and forget about hunger"
- And finally a very bad news: Scarlett Johansson is home with Ryan Reynolds
Written by Oriolrc the Sept. 29, 2008 with 221 points.
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# 1, PapaPitufo
What hurts me most today is what Yohansson of Scarlett.
Sniff
Black Monday ...