Question

For a whole life annuity on (70), you are given: The annuity pays 50 every 6 months with the first payment made immediately. Deaths are uniformly distributed over each year of age. Mortality follows the Standard Ultimate Life Table. i=0.05 Calculate the expected present value of the annuity payments.

Answer 1

To calculate the expected present value of the annuity payments, we need to use the mortality rates from the Standard Ultimate Life Table and the given interest rate.

Step-by-step explanation:

To calculate the expected present value of the annuity payments, we need to use the mortality rates from the Standard Ultimate Life Table and the given interest rate. Here are the steps:

1. Calculate the present value factor for each payment using the formula: P = (1 - (1 + i)^(-n)) / i, where i is the interest rate and n is the number of periods.
2. Calculate the probability of a person surviving to each age using the mortality rates from the life table.
3. Multiply the probability of survival by the present value factor for each age to get the present value of the annuity payments at that age.
4. Sum up all the present values to get the expected present value of the annuity payments.

For example, if the annuity pays 50 every 6 months, and the interest rate is 0.05, you would calculate the present value factor for each payment, then multiply it by the probability of survival to each age, and sum up all the present values to get the expected present value.