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

Solution:

Find the PV (retirement) for the 15-year benefit payment:

$20,000(PVIFA7%, 15 years) = $182,158.28.

Find the average payment required to collect the following sum for a span of 20 years:

Annual payment = $182,158.28/ FVIFA 7%,

20 years = $4,443.37

$4,443.37 is Barrington's annual pension contribution to the nearest dollar for Mr. Rossiter

The annual pension contribution to the nearest dollar for Mr. Rossiter is $4443

Explanation:

From the given data,

we have to find PV( at retirement) of the 15 year pension payment

PV = FV / (1+r)ⁿ

      = $20000( PVIFA 7%, 15 years)

After calculating we get,

  PV = $182,158.28

Now, we have to find the annual payment to accumulate the above  amount over 20 years.

Annual payment = $182,158.28/ FVIFA 7%, 20 years

                             = $4,443.37

Therefore, The annual pension contribution to the nearest dollar for Mr. Rossiter is $4443