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Composition of Interest Rates

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Composition of interest rates
In economics, interest is considered the price of money, therefore, it is also subject to distortions due to inflation. The nominal interest rate, which refers to the price before adjustment to inflation, is the one visible to the consumer (i.e., the interest tagged in a loan contract, credit card statement, etc). Nominal interest is composed by the real interest rate plus inflation, among other factors. A simple formula for the nominal interest is: i = r + π
Where i is the nominal interest, r is the real interest and π is inflation.
This formula attempts to measure the value of the interest in units of stable purchasing power. However, if this statement was true, it would imply at least two misconceptions. First, that all interest rates within an area that shares the same inflation (i.e. the same country) should be the same. Second, that the lender knows the inflation for the period of time that he/she is going to lend the money.
One reason behind the difference between the interest that yields a Treasury bond and the interest that yields a Mortgage loan is the risk that the lender takes from lending money to an economic agent. In this particular case, the US government is more likely to pay than a private citizen. Therefore, the interest rate charged to a private citizen is larger than the rate charged to the US government.
To take into account the information asymmetry aforementioned, both the value of inflation and the real price of money is changed to their expected values resulting in the following equation: it = rt + 1 + πt + 1 + σ
Where it is the nominal interest at the time of the loan, rt + 1 is the real interest expected over the period of the loan, πt + 1 is the inflation expected over the period of the loan and σ is the representative value for the risk engaged in the operation.

[edit] Cumulative interest or

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