# Understanding Interest Rates

The interest rate on a loan is the percentage calculated according to predefined conventions, which measures in summary, over time, the return to the lender or the cost to the borrower on the timing of cash flows of the loan. It is usually expressed in annualized format or monthly rates.

In general, the rates in all fixed income markets of the world are formed primarily in relation to the most liquid instruments and spread to other instruments through two processes. And these entail arbitration, whose principle is made from scratch (without stock). While no substitution involves fund managers disposing of an asset they have in stock and buying another they consider less expensive in relative terms.

The general interest rate formula is Z = k \ cdot \ frac (p) (100) \ cdot \ frac (t) (T) \ qquad \ text (or) \ qquad Z = k \ cdot i \ cdot \ frac (t) (T). Where k = capital in monetary units, p = rate of interest as a percentage, i = interest rate as a pure numerical value (1% = 0.01), t = return on time and T:  days splitter.

The correct use of the interest rate formula with respect to ‘t’ days and days splitter T is always an indication of the importance of calculation. The calculation indicates how to proceed with maturities under one year.

The interest rate markets are the most important capital markets of the world, well ahead of other financial markets, not only because of volume trading but basically due to their economic importance. It is common to separate them into money markets for short-term or long term bond markets.

The interest rate market was created in the first half of the nineteenth century, making it the oldest capital market. The concept of interest rate applies to all transactions including financial instruments that are generally described by convention as savings products (savings accounts, bonds, etc).

For the neoclassical models, the interest rate is the remuneration of abstinence: which entails forfeiting immediate consumption in order to save. The interest rate is the price of time and the reward of waiting. For John Maynard Keynes, the interest rate is the reward for forgoing liquidity. “It measures the reluctance of holders of money to exercise their right to dispose it at any time”.

The market for government bonds provides the interest rate curve without risk. For short-term rates, the market is the controller of the swaps and futures via IBOR (medium and long term).

The recovery rate of an instrument with a risk of credit (loan, bond, etc.) takes place in updating the schedule of financial flows of an instrument with the discount factors applicable to the bonds. In addition to adding a liquidity premium, that is an estimate of the cost of negotiation of an instrument. And by adding an estimate of the expected value of the risk of default by the borrower during the loan period.

The difference in yield to maturity shifts the curve of zero-coupon bonds to arrive at the price shown on the market. An  interest rate spread is commonly used to compare the relative values of various instruments.

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