Question $23(7$ marks$)$

Jack inherits $$200000$ and invests it in an account earning interest at a rate of $0\mathrm{.}5\%$ per month. Each month, immediately after the interest has been paid, Jack withdraws $$2000.$

The amount in the account immediately after the $n$th withdrawal can be determined using the recurrence relation

$A_n=A_{n-1}(1\mathrm{.}005)-2000$

Where $n=1,2,3,q,$ and $A_0=200000$

$($a$)$ Calculate the amount of money in the account immediately after the ${70}^{th}$ withdrawal.