Interest rate

From WilmottWiki

The interest rate is an amount, quoted as a percentage, paid as compensation for the loan of money. The amount of the loan is known as the principal. Interest is paid by banks when money is deposited there, and by corporates when you buy their bonds.

There are several classifications of interest rate.

Contents 1 Simple and compound interest 1.1 Simple interest 1.2 Compound interest 2 Discrete and continuous interest 2.1 Discrete interest 2.2 Continuous interest 3 Fixed and floating rates 3.1 Fixed rate 3.2 Floating rate

Simple and compound interest

Simple interest

Simple interest is when interest is only paid on the principal. For example, 4% paid annually on $100 will result in interest payments of $4 every year.

Compound interest

Compound interest is when interest is paid on both the principal and the accumulated interest. For example, 4% compound interest on $100 will after years becomes $. Generally, if an annualized rate of $r$ is paid $m$ times a year for $n$ years on $1 then the resulting amount would be .

Discrete and continuous interest

Discrete interest

Is interest that is paid in lump sums. The above two examples are of this form.

Continuous interest

If the interest is accumulated continuously then the Taylor series expansion of as results in . Since most option theory is based on continuous-time models the definition of interest there is usually of the continuous variety.

Fixed and floating rates

Fixed rate

When the interest rate is a specified amount, known in advance, it is called "fixed."

Floating rate

Floating rates are when interest payments are set according to a specified formula at sme time in the future. At the time of entering into floating-rate contracts the amount of the payment(s) will not be known.