Congratulations! You just won the $$1,000,000$ grand prize from a trivia game show. The producers of the show offer you two options to receive your winnings: Option $1$: receive $$50,000$ per year for $20$ years with the first payment occurring in one year Option $2$: receive $$650,396\mathrm{.}82($the present value of the annuity$)$ today What interest rate makes you indifferent between the two options?

$7\mathrm{.}2\%$

$1\mathrm{.}4\%$

$4\mathrm{.}5\%$

There is no interest rate that makes you indifferent. You should always prefer option $2.$