Each year a salesperson is paid a bonus of $2000 which is banked into the same account. It earns a fixed rate of interest of 6% p.a. with interest being paid annually. The total amount in the account at the end of each year is calculated as follows:
A0= 2000
A1= A0 x 1.06 + 2000
A2= A1 x 1.06 + 2000 and so on.
a) Show that A2= 2000 + 2000 x 1.06 + 2000 x (1.06)^2.
b)Show that A3= 2000[1 + 1.06 + (1.06)^2 +(1.06)^3].
c) Find the total bank balance after 10 years, assuming there are no fees or charges.

Question

Each year a salesperson is paid a bonus of $2000 which is banked into the same account. It earns a fixed rate of interest of 6% p.a. with interest being paid annually. The total amount in the account at the end of each year is calculated as follows:
A0= 2000
A1= A0 x 1.06 + 2000 
A2= A1 x 1.06 + 2000 and so on. 
a) Show that A2= 2000 + 2000 x 1.06 + 2000 x (1.06)^2.
b)Show that A3= 2000[1 + 1.06 + (1.06)^2 +(1.06)^3].
c) Find the total bank balance after 10 years, assuming there are no fees or charges.