Susan would like to receive $$50,000$ in the first year of her financial independence at age $60.$ After this first income payment, she is content with her annual income growing at the rate of $2\%$ per annum$$below$$the rate of inflation. She would like this income to be paid indefinitely. She expects inflation to be $2\%$ per year and her investments to achieve nominal returns of $8\%$ per year $($compounded yearly$).$ Assuming that all calculations are to be performed in $$real$$ terms, how much does she need to save for financial independence $($to the nearest dollar$)?$