Final answer:
To calculate the expected value of an annuity, one must determine the present value of future payments using the formula that accounts for the interest rate and time, then sum these present values up. If life expectancy affects the annuity, this must be taken into account.
Step-by-step explanation:
To calculate the expected value of an annuity paid over a lifetime, which is often referred to as a life annuity, you need to determine the present value of each future payment and then sum them up. Annuities are a series of equal payments made at regular intervals, and the present value of each payment can be determined using the formula for present discounted value. The present discounted value takes into account the time value of money, which reflects the idea that a dollar today is worth more than a dollar in the future because of its potential earning capacity.
For example, to calculate the present value of a single future payment, you can use the formula:
Present Value = Future Value / (1 + interest rate)time
Here, the Future Value is the amount of the payment, the interest rate is the discount rate, and time is the number of periods until the payment is received. In Yelberton's scenario, the interest rate is 6%, and the time would be the number of years until each annuity payment is expected to be received after retirement.
To calculate the overall expected value of the annuity, you need to follow these steps:
- Calculate the present value of each annuity payment expected to be received.
- Sum up all the present values to get the total present value of the annuity.
- If the annuity is contingent on survival, consider life expectancy and adjust the calculation based on the probability of living to each payment period.
This approach takes into account the probability of receiving each payment given life expectancy and understood as an expected value. An exact calculation would also involve integrating the survival probabilities associated with each payment period.