$1$ point$)($Exercise $3\mathrm{.}30)$ A beneficiary receives a $ $10,000$ life insurance benefit. If the beneficiary uses the proceeds to buy a $15-$year annuity$-$immediate, the annual payout will be $$1132\mathrm{.}87.$ If a $30-$year annuity$-$immediate is purchased, the annual payout will be $$846\mathrm{.}71.$ Both calculations are based on an annual effective interest rate of ii$.$ Find ii$.$