John aims to pay a certain amount of money each month into a pension fund. He plans to pay \(\pounds 100\) in the first month, and then to increase the amount paid by \(\pounds 5\) each month, i.e. paying \(\pounds 105\) in the second month, \(\pounds 110\) in the third month, etc.
If John continues making payments according to this plan for 240 months, calculate
(a) how much he will pay in the final month,
(b) how much he will pay altogether over the whole period.
Rachel also plans to pay money monthly into a pension fund over a period of 240 months, starting with \(\pounds 100\) in the first month. Her monthly payments will form a geometric progression, and she will pay \(\pounds 1500\) in the final month.
Calculate how much Rachel will pay altogether over the whole period.