$1\mathrm{.}1$ You sider the following two accounts for an investment of $$500,000$ for $9$ years:

With an annual rate of $6\%$ with continuous compounding.

With an annual rate with quarterly compounding that will yield the same amount as

in account $1$ after $9$ years.

Calculate the annual rate with quarterly compounding that is used in account $2.$

$1\mathrm{.}2$ A T$-$bill matures in exactly $219$ days. It's face $($par$)$ value is $$1,000\mathrm{.}00.$ The T$-$bill

trades right now for $$970\mathrm{.}4455.$

Calculate the annual rate on the T$-$bill. Use continuous compounding.

$1\mathrm{.}3$ You invest $$100,000\mathrm{.}00$ in an account that pays an annual rate of $8\%$ with

continuous compounding? Calculate the amount of time that it will take for your

account to have $$300,000$ in it$.$ The answer may not be an integer.