6  Time value of money

The world of finance and investments has as its basis the time value of money, the assumption that one pound/euro/dollar is worth more today than it will be sometime in the future. For example, one unit of whatever currency can be invested to give an annual rate of return r and grow to 1 + r after one year. This means that £1 today is worth 1 + r pounds in one year. After two years £1 grows to (1 + r)(1 + r) = (1 + r)2. After n years it becomes (1 + r)n. The rate of return r is a number. If r = 0.1 it is the equivalent of 10 per cent.

The present value PV of an investment with a rate of return equal to r per year grows to a future value FV in the course of n years:

The value of receiving FV in n years’ time is PV:

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