Suppose you get for free one of following two securities: $($a$)$ an annuity that pays $$10,000$ at the end of each of the next $6$ years; or $($b$)$ a perpetuity that pays $$10,000$ forever,$$but it does not begin until $10$ years from now$($i$.$e$.,$ the first cash payment from this perpetuity is $11$ years from now$).$Which security would you choose if the annual interest rate is $5\%?$ Does your answer change if the interest rate is $10\%?$ Explain why or why not.$$