Pensions and Annuities. Joe Taylor. Basic Outline. Quick overview of pensions and how they came to be Annuities defined and studied How to calculate an annuity Examples from Actuarial Tests for Exam FM/2 on annuity calculations. What is a Pension?.
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Pensions and Annuities Joe Taylor
Basic Outline • Quick overview of pensions and how they came to be • Annuities defined and studied • How to calculate an annuity • Examples from Actuarial Tests for Exam FM/2 on annuity calculations
What is a Pension? • An arrangement to provide people with an income when they are no longer earning a regular income from employment • Often in form of life annuity • Employment based pensions • Social and State pensions • Disability pensions
Defined Benefit Plans • Benefit is calculated by a predetermined formula • Dollars Times Service Plan • If the plan states that the person will get $100 per month for each year of service, a person with 30 years of service would get $3000 per month • Final Salary Plan • Final Average Pay • Interest Problems • Early Retirement provisions
Funded vs. Unfunded • Unfunded: no assets are set aside • Usually paid for out of current taxes • U.S. Social Security • Funded: contributions are regularly made by the employer or employee prior to the maturity of the pension • Most private benefit plans
Defined Contribution Plans • Contributions made into accounts for each individual • Usually reinvested into a stock market • Retirees usually cash out at retirement and purchase an annuity • Risk/Reward situation • IRAs 401(k)s
Pensions in USA • “promises” made to veterans of Revolutionary and Civil War • Eventually were offered by local governments in late 1800’s • Popular during World War II • Wage freezes prohibited increases in pay • World wide crisis: aging population + lower birth rates =big trouble
Annuities • A financial contract in the form of an insurance product according to which an issuer makes a series of future payments to a buyer in exchange for immediate payment of a lump sum (or a series of payments) prior to the onset of the annuity
Annuity Immediate • Payments made at end of year • v= present value of first payment • n= number of payments • i=interest rate • d= discount rate
Future Value Annuity Immediate Perpetuities
Actuarial Exam Question • A perpetuity immediate pays X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian’s share of the present value of the original perpetuity is 40%, and Jeff’s share is K. • Calculate K • Answer: 36%
Annuity Due • Very similar to annuity immediate, but payments are made at the beginning of each time period • Multiply annuity immediate by i/d=1+i
Example • Given i=5% and n=10, find annuity due present value. • Notice this is different than previous answer of 7.7217
Sample Actuarial Question • Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. • The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account after 20 years. • Find X • Answer: 6195
Increasing Annuities with Terms in Arithmetic Progression An annuity where payments increase by 1 unit(or more) after each payment If i= 5% and n= 4
Decreasing Annuities with Terms in Arithmetic Progression • This is an annuity where each payment decreases by an equal amount from the previous payment • All other formulas for the decreasing annuity and increasing annuity can be derived from these two equations
Actuarial Example • The present value of a 25-year annuity-immediate with a first payment of 2500 and decreasing by 100 each year thereafter is X. Assuming an annual effective interest rate of 10%, calculate X • Answer:
Annuities with Terms in Geometric Progression • An annuity where each payment increases by g% over the previous payment • Using geometric series(we all learned it but probably forget):
One Last Example • Given i=10%, find PV of sequence of payments of
Works Cited • }http://en.wikipedia.org/wiki/Pension • }http://en.wikipedia.org/wiki/Life_annuity • }Emms, Paul. "Income Drawdown Schemes for a Defined Contribution Pension Plan." The Journal of Risk and Insurance 75.3 (2008): 739-61. Print. • }Horneff, Wolfram. "Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities." The Journal of Risk and Insurance75.4 (2008): 1019-037. Print. • }Antolin, Pablo. "Private Pensions and THe Financial Crisis: How to Ensure Adequate Retirement Income from DC Pension Plans."OECD Journal 2 (2010): 153-71. Print. • }Hassett, Matthew, Toni Garcia, and Amy Steeby.ACTEX Study Manual SOA Exam 2. United States: ACTEX Publications, 2010. Print.