Final answer:
A40 is calculated using the formula A40 = S(40) * (1 + i)-1 * (A41 + 1), resulting in A40 = 0.7283 when substituting the provided values.
Step-by-step explanation:
The question provided is asking for the calculation of the actuarial present value of life annuities, specifically A40, based on given mortality rates and interest rate. The values provided include S(40) as the probability of survival from age 40 to 41 and S(41), along with the indicated interest rate i, and the actuarial present value for age 41, A41. To calculate A40, we must account for the probability of surviving the year from age 40 to 41, as well as the assumption that deaths are uniformly distributed over each year of age.
To find A40, we can use the following formula:
A40 = S(40) * (1 + i)-1 * (A41 + 1)
We know S(40) = 0.500, S(41) = 0.475, and A41 = 0.54 with i = 0.06. Substituting these values in, we have:
A40 = 0.500 * (1 + 0.06)-1 * (0.54 + 1) = 0.500 * (1/1.06) * (1.54) = 0.7283.
This represents the actuarial present value of the life annuity at age 40. Since more information about the uniform distribution of deaths is not given, and we are not calculating a life insurance benefit, the extra information is not directly used in our calculation for A40.