Use the information in the following table to determine the time value of the August

$160$ put option assuming American options. The option prices were observed for a

stock on July $6$ of a particular year. Ignore dividends on the stock. The stock is

priced at $$165\mathrm{.}13.$ The expirations are August $21$ and October $16.$ The risk free

rates are $5\mathrm{.}50\%$ for August and $5\mathrm{.}88\%$ for October.

$$0$

$$2\mathrm{.}75$

$$2\mathrm{.}18$

$$3\mathrm{.}20$