The question deals with pricing and the risk margin is 8% of the risk premium and instead of 0.08 they use 1.08 and I don't understand why.

Solution:

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For this question, the definition of the Risk Premium (RP) is what is important. The RP is the portion of the premium which covers the expected cash outflow due to claims. Therefore, if we find the present value of the RP it is equivalent to the expected present value of claims.

Now consider the following equation:

\(EPV(OP) = EPV(Claims) + EPV(Expenses) + EPV(Profit) + EPV(Risk)\)

For this question, these values are as follows: (where i is the effective monthly rate)

\(EPV(OP) = 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Claims) = PV(RP) = RP\ddot{a}_{\bar{12|}i}\)

\(EPV(Expenses) = 150 + 0.05EPV(OP) = 150 + 0.05 \times 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Profit) = 0.1EPV(OP) = 0.1 \times 275 \ddot{a}_{\bar{12|}i}\)

\(EPV(Risk) = 0.08PV(RP) = 0.08 \times RP\ddot{a}_{\bar{12|}i}\)

Thus, when you combine the \(EPV(Claims)\) and the \(EPV(Risk)\) you end up with the 1.8 times the present value of the RP.

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