You are planning for retirement and would like to know how much you need to save each year to meet your goals. You plan to start saving at $25$ years old, and save through retiring the year you turn $65.$ The following year you would like to draw $$50,000$ per year starting for $25$ years. Interest rates are currently $5\%,$ but you want to plan for them to be $7\%$ during retirement.

What is the present value of the annuity you would need at age $65$ for your annual retirement draws?

How much will you need to save each year between ages $25$ and $65$ to meet these goals?