At the end of each year, a salesperson is paid a bonus of $2000 which is always deposited 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 will be:
A1=2000A2=A1×1.06+2000A3=A2×1.06+2000 and so on.
a. Show that A3=2000+2000×1.06+2000×(1.06)2 .
b. Show that A4=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 withdrawals.