You just turned $30$ years old and you are hoping to live until your $95$th birthday. You are planning to save enough to earn a retirement pension of $$75$k per year $($in real terms$)(*)$ beginning on your $65$th birthday, including a government pension of $$12$k per year $($expected to be adjusted for inflation over time$).$ Assume an investment return of $7\%$ and an inflation of $2\%.$

Your salary is now $$100$K for the coming year. You expect it to be steadily adjusted for inflation and to work until your $65$thbirthday. $($Assume that your salary is paid at the end of each year$).$ If you start contributing to your pension fund at the end of the coming year, what fraction of your salary should you be saving?

This means that you want to have sufficient funds to purchase $($every year$)$ an amount of goods that would cost $$75$k today, taking inflation into account $($Attempt using the growing annuity formula$).$