Olivia Norman invests $$100,000$ today in an investment that earns $15$ percent per year $($compounded annually$)$ for $20$ years. The average inflation rate is expected to be $2\mathrm{.}5$ percent per year. She will have much more than $$100,000$ in $20$ years BUT what would this future amount be if expressed in today's dollars?

$$1,054,509$

$$1,021,440$

$$986,673$

$$972,114$

$$998,802$

Please solve, list all formulas used and steps.