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Foundations of Pension Mathematics
Pension Mathematics: Securing the Golden Years
Pension mathematics is the study of valuing long-term promises made to employees for their retirement. The central problem is: “How much money do we need today to pay someone $X amount every year starting 30 years from now?“
1. The Concept of an Annuity
An Annuity is a series of payments made at fixed intervals. In actuarial science, we weight these payments by survival probabilities and discount them back to the present.
2. The Impact of Interest Rates
The discount rate is the most sensitive variable in pension math. Even a tiny change in the interest rate can cause massive swings in the reported pension liability.
Impact of Interest Rates on Pension Present Value
| Assumed Interest Rate | Annual Payment | Duration | Total Present Value |
|---|---|---|---|
| 1.0% | $10,000 | 20 years | $180,170 |
| 2.0% | $10,000 | 20 years | $163,514 |
| 3.0% | $10,000 | 20 years | $148,775 |
| 4.0% | $10,000 | 20 years | $135,903 |
| 5.0% | $10,000 | 20 years | $124,622 |
3. Funding and Solvency
A pension plan is “Fully Funded” if its current assets equal its future liabilities. Actuaries perform periodic “Valuations” to ensure the fund remains solvent.
💡 Professor’s Tip
In a “Low Interest Rate Environment,” pension funds face a dual crisis: their liabilities increase because of lower discounting, while their investment returns also tend to drop. This is the actuary’s biggest challenge today.