Michael L. answered • 09/13/26
UT Austin Grad | Math, Writing & Test Prep Tutor Who Cares!
Giulianna is age 35 in 2020 and will retire at age 60, so she will work for 25 years.
Salary in 2020 = $70,000
Salary growth = 3%
Discount rate = 6%
Pension = 2% of final salary for each year of service
Retirement period = 20 years
Payments are made at the beginning of each retirement year, so we use an annuity-due factor.
First, calculate the 20-year annuity-due factor at 6%:
PV annuity due factor
= (1 - 1/1.06^20) / .06
= 12.1581
Projected final salary:
Final salary = 70,000(1.03)^24
= $142,295.59
The exponent is 24 because the first salary is already $70,000 in year 1, so there are 24 salary increases over 25 years of employment.
- ACCUMULATED BENEFIT METHOD
Under this method, the pension earned to date is based on the employee's current salary rather than projected final salary.
END OF 2020
After one year, accumulated pension benefit is:
Annual pension = .02(1)($70,000)
= $1,400
Value of this pension at retirement:
$1,400(12.1581)
= $17,021.36
At the end of 2020, retirement is 24 years away:
Required funding = 17,021.36 / 1.06^24
= $4,203.91
Therefore, required accumulated funding at the end of 2020 is:
$4,203.91
END OF 2021
2021 salary:
70,000(1.03) = $72,100
She now has 2 years of service, so:
Annual pension = .02(2)($72,100)
= $2,884
Value at retirement:
2,884(12.1581)
= $35,062.41
At the end of 2021, retirement is 23 years away:
Required funding = 35,062.41 / 1.06^23
= $9,179.66
Therefore:
2020 required funding = $4,203.91
2021 required funding = $9,179.66
If the 2020 fund earns 6%, the additional contribution needed at the end of 2021 is:
9,179.66 - 4,203.91(1.06)
= $4,723.52
- PROJECTED UNIT METHOD
Under the projected unit method, each year of service earns 2% of the projected final salary.
Projected final salary:
$142,295.59
Benefit earned for each year of service:
.02($142,295.59)
= $2,845.91 per year during retirement
Value at retirement of one year's earned benefit:
2,845.91(12.1581)
= $34,600.93
END OF 2020
One unit of benefit has been earned.
Required funding:
34,600.93 / 1.06^24
= $8,545.69
END OF 2021
Two units have now been earned:
2($34,600.93)
= $69,201.85 at retirement
Discount this for 23 years:
69,201.85 / 1.06^23
= $18,116.86
Therefore:
2020 required funding = $8,545.69
2021 required funding = $18,116.86
The additional contribution required at the end of 2021 is:
18,116.86 - 8,545.69(1.06)
= $9,058.43
- LEVEL CONTRIBUTION METHOD
Under this method, equal annual contributions are made over Giulianna's 25-year working period.
First calculate the total annual pension at retirement:
Annual pension
= .02(25)($142,295.59)
= $71,147.79 per year
Value of the entire pension at retirement:
71,147.79(12.1581)
= $865,023.16
Now determine the equal annual contribution that will accumulate to $865,023.16 after 25 years.
Future value annuity factor:
[(1.06^25 - 1) / .06]
= 54.8645
Annual contribution:
865,023.16 / 54.8645
= $15,766.53
Therefore, the same contribution is made each year:
2020 contribution = $15,766.53
2021 contribution = $15,766.53
The accumulated fund balances would be:
End of 2020:
$15,766.53
End of 2021:
15,766.53(1.06) + 15,766.53
= $32,479.06
FINAL ANSWERS
Accumulated Benefit Method:
End of 2020: $4,203.91
End of 2021: $9,179.66
Projected Unit Method:
End of 2020: $8,545.69
End of 2021: $18,116.86
Level Contribution Method:
Annual contribution in 2020: $15,766.53
Annual contribution in 2021: $15,766.53
Accumulated level-contribution fund:
End of 2020: $15,766.53
End of 2021: $32,479.06
The main difference is that the Accumulated Benefit Method uses salary earned to date, the Projected Unit Method uses projected final salary but recognizes benefits as service is earned, and the Level Contribution Method spreads the cost evenly over the employee's entire working period.
