Guaranteed death benefit

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Hi, could you please explain how to approach this question? There's no memo (from an old exam).

Is it correct to assume that for all the years before the final year of the policy, the EPV of the death benefit would just be calculated using the standard decreasing term assurance formulas with duration of 24 years, and in the final year when the guarantee 'kicks in', the death benefit would be the accumulated value of all of the premiums at 3% interest at the start of the final year multiplied by the relevant probability of dying in the last year and then discounted back to the start of the policy, i.e. Death Benefit in final year = (P x (accumulation of annuity in advance for 15 years @3%, independent of mortality, so the Sn formula)) x (1.04)^9 and then the EPV would be V^25 x (24_P_40 select) x q_25 ? x Death Benefit in the final year?

by (2.9k points)

You are correct except for the last part of your death benefit amount calculation:

x (1.04)^9

You would instead write:

x(1.03)^10

Because you are still accumulating the premiums at 3% (and then discounting them at 4%) and the benefit is paid at the end of the year of death so you need to accumulate your premiums to the end of year 25.