5.4 Recurrence Relations of the form Un+1 = aUn

Suppose you invested £500 in an account which paid 8% per annum (each year, shortened to p.a.), the interest being credited to the account at the end of each year.

The amount is being compounded annually at a rate of 8%.

What we have here is, in fact, compound interest.

Since the £500 is increasing by 8%, this means that we can apply a growth factor of 1.08 to the £500.

At the end of year 1 the account is worth £500 x 1.08 = £540.

At the end of year 2 it is no longer £500 which is being increased, but £540.

The account is now worth £540 x 1.08 = £583.20.

At the end of year 3 we have £583.20 x 1.08 = £629.856 and so on.

Each year we multiply what we had the year before by 1.08.

A perfect recurrence relation!