A bank has an account for investors. Interest is added to the
account at the end of each year at a fixed rate of 5% of the amount
in th account at the beginnning of that year. A man deciddes to
invest $x at the beginning of one year and then a further $x at the
beginning of the second and each subsequent year, he also decides
that he will not draw any money out of the account, but just leave
it and any interest to build up. Show that, at the end of n years,
when the interest for the last year has been added, he will have a
total of $ 21(1.05^n - 1)x in his account.