An insurance company has a merit rating system for customers who have not filed a claim in the previous year. For each year that a customer does not file a claim, their rate is reduced by 15%, and a credit of $5 is awarded. If a customer did not file a claim in the nth year, which equation shows the customer's rate in the (n + 1)th year as a function of their rate in the nth year? A. F(n + 1) = f(n) - 0.15f(n) - 5 B. F(n + 1) = f(n) - 0.15f(n) + 5 C. F(n + 1) = f(n) - 0.15f(n) - 10 D. F(n + 1) = f(n) + 0.15f(n) - 5

B. Fₙ₊₁ = Fₙ - 0.15Fₙ + 5

Step-by-step explanation:

The options above are examples of recurrence relations where the present state Fₙ₊₁ is dependent on the previous state Fₙ.

For each year that a customer does not file a claim, their rate is reduced by 15%

Fₙ-(15% of Fₙ)= Fₙ-0.15Fₙ

A credit of $5 is also awarded, therefore:

Fₙ - 0.15Fₙ + $5

Therefore If a customer did not file a claim in the nth year, the customer's rate in the (n + 1)th year as a function of their rate in the nth year is given by:

Fₙ₊₁ = Fₙ - 0.15Fₙ + 5

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