[CAS4-F82:19] Experience on certain $20,000 luxury sports cars shows probabilities, $q_x$, of theft within a one year period to be as follows:
Age $x$ $q_x$
0 0.15
1 0.10
2 0.08
3 0.03
The car neither appreciates nor depreciates in value and, once stolen, is never recovered.
A 3 year non-cancelable (except for theft of the vehicle) theft policy that provides for the payment of an annual level premium $P$ is issued on one of these cars when purchased new.
If the claim is payable at the end of the year of theft and interest is earned at an effective annual rate of 10%, what is $P$?
A. Less than $2,050
B. At least $2,050, but less than $2,150
C. At least $2,150, but less than $2,250
D. At least $2,250, but less than $2,350
E. At least $2,350
