You are preparing for retirement in $40$ years. The average inflation is expected to be $4\mathrm{.}3\%$ each year for the next $40$ years.

a$)$ If you have saved $$1$ million in your retirement account when you retire, what is the purchasing power of that $$1$ million in todays $(2024)$ value?

b$)$ How much money do you need in your retirement account at the end of $40$ years to have the purchasing power of $$2$ Million today?