$(1$ point$)($Exercise $3\mathrm{.}30)$ A beneficiary receives a $$10,000$ life insurance benefit. If the beneficiary uses the proceeds to buy a $8-$year

annuity$-$immediate, the annual payout will be $$1766\mathrm{.}65.$ If a $16-$year annuity$-$immediate is purchased, the annual payout will be

$$1158\mathrm{.}82.$ Both calculations are based on an annual effective interest rate of $i.$ Find $i.$

$i=$