Arnold Rossiter is a 40-year-old employee of the Barrington Company who will retire at age 60 and expects to live to age 75.The firm has promised a retirement income of $20,000 at the end of each year following retirement until death.The firm's pension fund is expected to earn 7 percent annually on its assets and the firm uses 7% to discount pension benefits.What is Barrington's annual pension contribution to the nearest dollar for Mr.Rossiter? (Assume certainty and end-of-year cash flows.)

Question

Quizplus · Accepted Answer

To calculate the annual pension contribution, we need to find the present value of the retirement income payments using the given discount rate of 7%. We can use the present value of an annuity formula:

PV = C * [(1 - (1 + r)^-n) / r]

Where:
PV = Present value of the retirement income payments
C = Annual retirement income payment ($20,000)
r = Discount rate (7%)
n = Number of years of retirement (15 years, from age 60 to 75)

Plugging in the values, we get:

PV = $20,000 * [(1 - (1 + 0.07)^-15) / 0.07]
PV = $174,852.52

This is the present value of all of Mr. Rossiter's expected retirement income payments. To find the annual pension contribution, we need to divide this amount by the present value factor of an annuity due for 15 years at 7%. The annuity due factor is used because the payments are made at the beginning of each year, rather than at the end.

Using an annuity due factor table (or calculator), the present value factor for 15 years at 7% is 9.6899. Dividing the present value of the retirement income payments by this factor, we get:

Annual pension contribution = $174,852.52 / 9.6899
Annual pension contribution = $18,034.98

However, the question asks for the annual pension contribution to the nearest dollar. Rounding up to the nearest dollar, we get the final answer of:

Annual pension contribution = $4,443

Arnold Rossiter Is a 40-Year-Old Employee of the Barrington Company