Suppose you want to buy an annuity that would pay you $50,000$ per year for the rest of your life. How much should an insurance company charge you, if they assumed would live for $30$ years and they could get a $6\%$ return and a $10\%$ return? The PVA for $6\%$ is $13\mathrm{.}7648$ and $10\%$ is $9\mathrm{.}4269?$ Which assumed return allows for a cheaper annuity price and why?