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David's Agency sells an insurance policy offered by Pharoah Insurance Company for a commission of $$113$ on January $2,2025.$ In addition, David will receive an additional commission of $$10$ each year for as long as the policyholder does not cancel the policy. Based on David's significant experience with these types of policies, it estimates that policyholders on average renew the policy for $4\mathrm{.}5$ years, which results in an expected policy life of $5\mathrm{.}5$ years. It has no evidence to suggest that previous policyholder behavior will change.

$($a$)$

Determine the transaction price of the arrangement for David, assuming $105$ policies are sold.

Transaction price $

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