Interest Rates

An interest rate is the "Price of Time" or the "Time Value of Money".
An interest rate can represent the cost of borrowing or the reward from investing.
Interest rate products are often referred to as fixed income.
Interest rates are the single most important mechanism in the financial markets.
In order to understand interest rates accurately, you need to appreciate the different types:

Simple Interest

This is when the interest you receive is only based on the amount you initially invest.
If £50 is invested for 3 years at an annual interest rate of 5%, what is the total amount after 3 years?
The amount of interest in one year is £2.50 (50 * 5%)
The total amount after 3 years will be £57.50 (50.00 + 2.50 + 2.50 + 2.50).
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Compound Interest

This is when the interest you receive includes interest on your interest.
Compound interest is the concept of adding accumulated interest back to the principal so that interest can be earned on the principal plus the interest.
When an interest rate is compounded you need to know the compounding frequency (e.g. annually, semi-annually, monthly, daily etc).
If £100 is deposited into a savings account that is offering a compounding interest rate of 10% a year, what is the total amount after 3 years?
The amount of interest after one year is £10.00 (100 * 10%)
The amount of interest after two years is £11.00 ((100 + 10) * 10%)
The amount of interest after three years is £12.10 ((110 + 11) * 10%)
The total amount after 3 years will be £133.10 (100.00 + 10.00 + 11.00 + 12.10)
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Compound Interest - 2 Types

The precise meaning of a compounded interest rate depends on the way the interest rate is measured. There are two types:
Discretely - Interest is paid after a specific period of time (e.g. annual, semi-annual, quarterly, monthly, weekly, daily).
Continuous - Interest is paid continuously.

Nominal Interest

A nominal interest rate is an interest rate that is compounded over a period of less than 1 year.
These types of interest rates are not comparable unless they have the same compounding frequency.
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Effective Interest

An effective interest rate is an interest rate that is compounded every year.
These types of interest rates are directly comparable because they always have a compounding frequency of 1 year.
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Excel Functions

Complete List

Units

You must always make sure that all your arguments are in consistent units
You should always try and reduced all the values to the lowest denominator, probably monthly.
First we need to convert the annual interest rate to a monthly interest rate by dividing by 12
Next we need to convert the years into months by multiplying by 12.

Types of Interest Rate

1) Deterministic
2) Stochastic (or Random) - Processes where one state does not fully determine its next state (there is some randomness)
Financial models use stochastic models to value options on stock prices, bond prices and on interest rates (see Markov models)