Olivia receives an annuity for her eighteenth birthday. The annuity pays RM$2,000$ on her nineteenth birthday and continues with annual

payments on each of her birthdays until her $35$th birthday. Each year the payment increases by RM$500.$

Assume that the effective rate of interest is $4\mathrm{.}2\%$ p$.$a$.$

$($a$)$ If the money is kept in a fund, create a table indicating the cashflows.

$($b$)$ Find the price of the annuity.

$($c$)$ Once Olivia reaches the age of $35,$ she plans to immediately withdraw RM$5,000$ each year for $5$ years and then

continue to withdraw X each year for the next $5$ years. Find X$.$