Alice just turned $30$ and is considering buying a $35-$year term insurance policy with the following criteria:

Death benefit is $$100,000$ and paid at end of year of death.

APV is $$12,000.$

$i=5\%.$

Alice is looking into a similar insurance product with the only difference being that the death benefit is only $$10,000$ if she dies in the first three months. The APV of this product is $$11,865.$ Assuming constant force of mortality between integer ages, which value is closest to $q_{30}?$

$0\mathrm{.}0072$

$0\mathrm{.}0082$

$0\mathrm{.}0063$

$0\mathrm{.}0016$

$0\mathrm{.}0058$