The Laiterie de Coaticook in the Eastern Townships of Quebec produces several types of cheddar cheese. It markets this cheese in four$$ varieties: aged $2$ months, $9$ months, $15$ months, and $2$ years. At the$$ producer's store, $2$ kg of each variety sell for the following$$ prices: $ $6\mathrm{.}50,$ $ $10\mathrm{.}00$ comma $ $11\mathrm{.}00,$ and $ $12\mathrm{.}00,$ respectively. Consider the cheese$$ maker's decision whether to continue to age a particular$2-$kg block of cheese. At $2$ months, he can either sell the cheese immediately or let it age further. If he sells it$$ now, he will receive $ $6\mathrm{.}50$ immediately. If he ages the$$ cheese, he must give up the $ $6\mathrm{.}50$ today to receive a higher amount in the future.

What is the IRR$($expressed in percent per$$ month$)$ of the investment of giving up $ $65\mathrm{.}00$ today by choosing to store $20$ kg of cheese that is currently $2$ months old and instead selling $10$ kg of this cheese when it has aged $9$ months, $6$ kg when it has aged $15$ months, and the remaining $4$ kg when it has aged $2$ years?

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Part $1$

The IRR is

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enter your response here$\%$ per month. $($Enter your response as a percent rounded to two decimal$$ places.$)$