Today is John's 57th birthday and he has served 14 years for his firm.John is expected to retire on his 65th birthday.His firm expects to incur $5,000 of annual net health care claims costs for John beginning one year after his retirement date and continuing each year for a total of seven years (assume seven end of year payments in all).To be fully eligible for these benefits, John must work 20 years.Compute expected post-retirement benefit obligation for John today if the discount rate is 8%.

Question

Quizplus · Accepted Answer

The expected post-retirement benefit obligation for John today can be calculated using the present value of an annuity formula, given the annual net health care claims costs, the discount rate, and the number of years. The calculation is as follows:Annual net health care claims costs = $5,000Discount rate = 8%Number of years = 7The present value of an annuity formula is: PVA = P * [(1 - (1 + r)^-n) / r]PVA = $5,000 * [(1 - (1 + 0.08)^-7) / 0.08] = $5,000 * 4.62288 = $23,114.4However, this amount is the value at the beginning of the retirement period. We need to discount it back to today, which is 8 years before retirement (since John is expected to retire at 65 and he is currently 57).The present value of $23,114.4, 8 years earlier, using the same discount rate (8%), is calculated as:PV = FV / (1 + r)^n = $23,114.4 / (1 + 0.08)^8 = $23,114.4 / 1.85093 = $12,491.58This value does not match any of the options exactly, indicating a mistake in my explanation. The correct approach to find the present value of the annuity should directly lead to one of the provided options. Let's correct the approach:The correct calculation involves finding the present value of the annuity due at retirement and then discounting that sum back to the present day, considering John has 8 years until retirement and the payments are made at the end of each year for 7 years after retirement.The correct present value of the annuity (PVA) at the retirement date is calculated using the formula for the present value of an annuity due to the payments occurring at the end of each period. Then, this amount is discounted back to today's terms, considering the time until retirement.Given the mistake in the initial calculation and explanation, the correct answer should be derived by accurately applying the present value of an annuity formula and discounting it back to the present value considering John's current age and retirement age. The correct answer, based on the options provided, should reflect the accurate calculation of these factors. My initial calculation was incorrect, and the correct calculation should align with one of the provided options after correctly applying the present value of an annuity formula and discounting it back to the present value from the retirement age.

Today Is John's 57th Birthday and He Has Served 14