Ms$.$ Johnson is $40$ years old but appears much younger. She has applied for a life insurance policy that has a premium of $$25$ per $$1,000$ for age $40$ and $$15$ per $$1,000$ for age $35.$ On the application, Ms$.$ Johnson states her age as $35$ and purchases a $$20,000$ life insurance policy, issued for someone of that age. She dies unexpectedly $1$ year later at her actual age of $41.$ Calculate the death benefit that will be paid to Ms$.$ Johnson's beneficiary assuming the insurance company discovers the misstatement of age on the application.

A$.$ $$0$

B$.$ $$10,000$

C$.$ $$12,000$

D$.$ $$20,000$