Bloggs Ltd has to replace its widget-making machine in five years. The company estimates the new machine will cost

$30 000. It wishes to provide for this machine by putting aside a regular annual amount in a reserve. Natbank has offered the company two options:

a Deposit five equal amounts at the beginning of each year to earn 5 per cent compound interest.

b Deposit five equal amounts at the beginning of each year to earn an increasing compound interest rate of 2.5 per cent for the first year and increasing by 1 per cent each year after that.

Which option allows the company to put the least annual amount into a reserve, and what is that annual amount?