An insurance company would like to offer theft insurance for renters. The policy would pay the full replacement value of any items that were stolen from the apartment. Some apartments have security alarms installed. Such systems detect a break$-$in and ring an alarm within the apartment. The insurance company estimates that the a security system costs the renter an additional $$100$ per year. Assume that the dollar loss from a theft is $$10,000$ and that the insurance company is risk neutral and the renter would be willing to pay more than the expected loss to insure against the loss of theft. For a security system to be effective the renter must turn it on whenever he or one year theft insurance policy with that deductible amount for an apartment with a security system?

a$.$ $$192\mathrm{.}00$

b$.$ $$194\mathrm{.}29$

c$.$ $$195\mathrm{.}56$

d$.$ $$180\mathrm{.}00$