Annuity

Published on May 2016 | Categories: Types, School Work | Downloads: 44 | Comments: 0 | Views: 411
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Annuity calculations based on retirement age

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According to the Current Population Survey (CPS) conducted by the Bureau of Labor
Statistics on labor force participation in 2015, the average retirement age is estimated to be 64
years for men while women on average retire at the age of 62 years (Munnell). Based on the
background data, it can therefore be assumed that on average both men and women retire at
the age of 66, with a life expectancy of 15.86 years and 18.30 years respectively which is an
average of 17.08 years for both male and female employees.
Pay-out Obligations
Based on the background data, the average pension in Detroit is \$30,000 per year,
which is an ordinary annuity since it involves a series of equivalent payments that are made at
the end multiple periods. The value of the pay-out annuity at retirement for each employee
can therefore be calculated considering that at retirement, Detroit employees have an annuity
with an average pay-out of \$30,000 per year for 17.08 years. The present value of the pay-out
annuity at retirement at an interest of 6.3% is \$308,467.51 and the present value of the payout annuity at retirement at an interest of 8.9% is \$258,501.72. Given that the number of city
employees is 12,900, the city pension obligations after 30 years will be \$ 3,979,230,815 for
the 6.3% interest rate and \$3,334,672,198 for the 8.9% interest rate.
Annual Deposits
In order for an employee to accumulate the value of the pay-out annuity at retirement,
they will need to make annual deposits to their pension funds during their working life of 30
years. To accumulate the \$308,467.51 value of the pay-out annuity at retirement at an interest
rate of 6.3%, each employee must set aside \$3,700.41 annually. To accumulate the
\$258,501.72 value of the pay-out annuity at retirement at an interest rate of 8.9%, each
employee must set aside \$1,932.14 annually. The city payment obligations after 30 years will

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be \$1,432,060,139.13 for the 6.3% interest rate and \$747,739,017.70 for the 8.9% interest
rate.
Analysis
The analysis indicates that a city such as Detroit might prefer to use an 8.9% return
rather than a 6.3% return contingent on the fact that a higher interest rate results in lower
annual deposits which effectively reduce the value of principal repayments due to employees
in the future. If the city uses an 8.9% return but sees a 6.3% return, there will be a shortfall in
value available for annuity amounting to \$49,965.79 (\$308,467.51 - \$258,501.72). This
implies that the pay-out that can be supported by the accumulated value of the annuity will be
lower than the expected return. This will also result in a lower pay-out, which can be
computed as:

−n

1+r ¿
1−¿

annual payout=

r (PV )
¿

= (0.063 x \$258,501.72) ÷ (1 – (1 + 0.063)17.8)
= 16285.60836 ÷ 0.647781761
= \$25,141
This is a decline of \$4,859 of the pay-out value per annuity (\$30,000 - \$25,141).
If the city is to compensate the shortfall, the annual obligation to be incurred is \$62,686,534
(\$4,859 x 12,900) which is not substantial and will have a significantly negative impact on
the city finances.

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Work Cited
Munnell, Alicia. The average retirement age: an update. Center for Retirement Research at
Boston College, March 2015. <http://crr.bc.edu/wp-content/uploads/2015/03/IB_154.pdf> 3 Apr. 2016.

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