If we had lived in older, more primitive times, when slavery was still permissible and there was no uniform currency system in place, life – and the overall economic system – would still be simple (although quite unhygienic). For example, if Almathussela were to borrow 100 slaves from me on Tuesday, with the promise to pay me back during the next solar eclipse, being of rational mind (and Machiavellian disposition, although this situation predates Machiavelli by several centuries), I would ask for
adequate compensation upon the return of my 100 slaves. Perhaps a 10% surcharge, which would bring the total to 110 slaves?
The logic behind this is that I could have used the 100 slaves for my own purposes, perhaps for the construction of my latest temple. Therefore, friend Almathussela would have to sufficiently
convince me that it is more advantageous to lend him my 100 slaves than to use it for my own odious glorification. That is, he has to recompense me for the trouble of lending him 100 perfectly healthy slaves, and this payment is concretely realized through the 10% addition to my slavestock. Thus, the concept of
interest was born.
Of course, this example cannot possibly occur today. First of all, we are no longer inhumane, uncivilized and uncouth savages: a sound financial structure has long been institutionalized, and we utilize money instead of the primitive barter system. Second, and less importantly, technology has already evolved to the extent that enslavement of entire subhuman races is no longer necessary. Thus our situation has to be rephrased in less “exotic” terms, and we will try to approximate the flavor of the above example while incorporating this new concept of “money”, and how it affects interest.
Suppose now that John borrows P1000 from me in order to buy 100 apples at P10 per apple. After one year, he pays me back 105 apples (as compensation for the 100 apples I could have bought with my P1000), but in the same time period, the price of apple has gone up to P11 per fruit. Thus he has to pay me back a total of 105 apples x P11 per apple = P1155, where P155 is what we call the
nominal interest.
The only difference with this example and the previous one is that in the first one, raw goods are being traded with each other at a surcharge that we call the
real interest, while in the second one, the medium of exchange itself accrues “interest” during the time period. This is of course the
inflation rate. Thus, the nominal interest is composed, roughly of the real interest, plus the fluctuations due to the usage of a monetary medium of exchange – in this case the Philippine peso.
In the apple example, the real interest, as measured in apples, is
(105-100)/100 = 5%
And the inflation rate is
(P11-P10)/P10 = 10%
The nominal interest, as measured in pesos, is therefore
P155/P1000 = 15.5%
Which is actually equivalent to
105 (P11) = 105 (P10) (1 + 10%) = 100 (1 + 5%) (P10) (1 + 10%) = 1000 (1 + 5%) (1+ 10%)
More generally, we have the following equation, derived by Irving Fisher, a renowned
fisherman economist, which is called the Fisher Equation:
(1 + i) = (1 + r)(1 + pi)
where i is the nominal interest rate (the one that is usually quoted in business section of newspapers – the “official” surplus to the money one invests/lends) while r is the real interest rate (what one actually earns), and pi the inflation rate (the “fluff” added to the real interest rate but usually overlooked by investors because they think they’re really earning i, but they’re really earning r because the purchasing power of their money has gone down by a corresponding pi, along with everything else in the financial structure, and this is quite deceptive and makes one nostalgic for simpler, non-complicated times which do not require such hardcore mathematical analysis, or fundamental human rights and liberties). Anyway.
Recalling our basic lesson in the FOIL method, we multiply
First,
Outside,
Inside and
Last:
1 + i = 1 + r + pi + r*pi
The last term is usually disregarded because it is miniscule. For example in our example above using John as an example, the last term is 0.5%, which is really quite smallish to make any relevance in the actual world.
So the simplified form is as follows:
i = r + pi
Or
Nominal interest rate = real interest rate + inflation rate
This is a handy formula to remember. For example when your father exclaims at the breakfast table, amidst the pancakes, that yields on 10-year government bonds have gone up to 10%, and that his hard-earned investments are finally paying off, and you see the glaring headline at the front page that inflation rate is spiraling up to 15%, you can do some quick mental arithmetic and conclude that your father is quite dim.
Scoff, but quietly. Then ask for a raise in your allowance.
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