Using the Uniform Distribution of Deaths (UDD) method, the continuous equivalent premium rate contAx is computed as which formula?

Study for the SOA Fundamentals of Actuarial Mathematics (FAM) Exam. Prepare with flashcards and multiple choice questions with detailed explanations. Get ready for your future as an actuary!

Multiple Choice

Using the Uniform Distribution of Deaths (UDD) method, the continuous equivalent premium rate contAx is computed as which formula?

Under the Uniform Distribution of Deaths approach, converting a level annual premium to an equivalent continuous premium hinges on how discounting works for continuous versus discrete payments in a world with a constant force of interest δ (where δ = ln(1 + i)). The continuous premium rate contAx is the amount that, when paid continuously every year, yields the same expected present value as paying a level premium Ax at the end of each year. The relationship between the two discounting styles gives contAx = (i/δ) × Ax. Since δ < i for positive interest, the factor i/δ is greater than 1, so the continuous premium rate exceeds the annual premium, as expected when moving from discrete-year payments to a continuous stream. So the correct expression is contAx = (i/δ) × Ax.

Under the Uniform Distribution of Deaths approach, converting a level annual premium to an equivalent continuous premium hinges on how discounting works for continuous versus discrete payments in a world with a constant force of interest δ (where δ = ln(1 + i)). The continuous premium rate contAx is the amount that, when paid continuously every year, yields the same expected present value as paying a level premium Ax at the end of each year.

The relationship between the two discounting styles gives contAx = (i/δ) × Ax. Since δ < i for positive interest, the factor i/δ is greater than 1, so the continuous premium rate exceeds the annual premium, as expected when moving from discrete-year payments to a continuous stream.

So the correct expression is contAx = (i/δ) × Ax.

More practice questions