Could someone assist me with a series question?

[MinterMints]

the question goes:

on being retrenched from his job on 1 july keith received a cash payment of $60000. one year later he received his first annual payout of $30000 every year thereafter. Keith placed all his money in a suitcase as he recieved it and spent none. he hid the suitcase under his bed. on june 30 each year he would remove 25% of the money in his suitcase to spend on a holiday. Let An be the amount of money in his suitcase immediately after his nth first annual payout.

(i) show that keith has $75000 in his suitcase immediately after his first annual payment.
(ii) show that the amount of money in Keith's suitcase immediately after his third annual payment is given by A3 = 60000 x 0.75^3 +30000 (1+0.75+0.75^2)
(iii) show that An = 120000 - 60000(0.75^n)

I'm able to show part 1 and 2, im specifically stuck on part 3.
Anyone care to help me out? Cheers in advance.

[arii]

Hi there,

For (iii), you basically use the trend you found in (ii), except you do a general form instead.

You'll need to know the formula for the sum of infinite terms in a GP series.

I haven't figured out how to use the maths symbols and fractions on here yet so refer to attachment for the working out. 

[MinterMints]

Hey,

Thanks for the help.
appreciate it