Final answer:
An annuity is a financial product that provides a series of payments over a specified period of time. To find the single benefit premium for the annuity, calculate the present value of the annuity payments and divide it by the present value of a life insurance policy. The variance of Y can be defined in terms of actuarial notation as the sum of the squared differences between each individual annuity payment and the expected value of the annuity payments.
Step-by-step explanation:
An annuity is a financial product that provides a series of payments over a specified period of time. In this example, we are given a 20-year deferred annuity that is issued to an individual at the age of 40. The payment rate for the annuity is $1,000 at the age of 60 and increases continuously at a force of interest of 2%. The insurer pays a maximum of 30 years. To define and plot Y, we need to calculate the present value of the annuity payments using the given information and plot it over the time period.
To find the single benefit premium for the annuity, we need to calculate the present value of the annuity payments and divide it by the present value of a life insurance policy that pays $1,000 per year for 30 years starting at age 60. This will give us the premium amount that the individual needs to pay to receive the annuity.
The variance of Y can be defined in terms of actuarial notation as the sum of the squared differences between each individual annuity payment and the expected value of the annuity payments, divided by the number of payments.