An annuity table is a powerful tool for determining the present value of an annuity or any structured series of payments. Commonly utilized by accountants, actuaries, and insurance professionals, it evaluates how much money has been paid into an annuity and for how long to ascertain the amount due to an annuity buyer or annuitant. Tools like financial calculators or specialized software can also achieve this task.
Key Takeaways
- Accurate Value Calculation: An annuity table helps determine the present value of an annuity by applying a discount rate to future payments.
- Complex Made Simple: It simplifies calculations by providing an appropriate factor derived from the discount rate and payment periods.
- Enhanced Decision Making: You can use the factor to multiply the recurring payment dollar amount, leading to informed financial decisions.
How an Annuity Table Works
An annuity table offers a factor based on time and the discount (interest) rate. This factor, when multiplied by an annuity payment, helps to determine its present value. For instance, you could use an annuity table to calculate the present value of an annuity paying $10,000 annually for 15 years, assuming a consistent interest rate of 3%.
Given the concept of the time value of money, receiving a lump sum today is worth more than future payments because funds can be invested to earn interest. Thus, $10,000 today would be more valuable than receiving $1,000 annually for 10 years.
Present Value of an Annuity Formulas
The formula for calculating the present value of an ordinary annuity is:
P = PMT \times \frac{1 - (1 + r)^{-n}}{r}
Where:
- P = Present value of an annuity stream
- PMT = Dollar amount of each annuity payment
- r = Interest rate (discount rate)
- n = Number of periods in which payments will be made
Assume you’re evaluating an annuity yielding $50,000 per year for 25 years at a 6% discount rate against a lump sum of $650,000. The annuity’s present value would be:
PVA = $50,000 \times \frac{1 - (1 + 0.06)^{-25}}{0.06} = $639,168
In this example, since $639,168 is less than $650,000, choosing the lump sum is the more rational financial decision.
For an annuity due (payments made at the beginning of each period), modify the formula by multiplying with (1 + r):
P = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)
Using the annuity due adjustment, the value is:
P = $50,000 \times \left(\frac{1 - (1 + 0.06)^{-25}}{0.06}\right) \times (1 + 0.06) = $677,518
Here, the annuity due is a better option as it is worth more than the $650,000 lump sum.
Present Value of an Annuity Table
Rather than manually computing these values, an annuity table simplifies the process by providing pre-calculated factors for the second half of the formula. Here is a sample excerpt from a present value of an ordinary annuity table:
1|----|---------|---------|---------|---------|---------|---------|
2| n | 1% | 2% | 3% | 4% | 5% | 6% |
3|----|---------|---------|---------|---------|---------|---------|
4| 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 | 0.9434 |
5| 2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 | 1.8334 |
6| 3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7233 | 2.6730 |
7| 4 | 3.9020 | 3.8077 | 3.7171 | 3.6299 | 3.5460 | 3.4651 |
8| 5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 | 4.2124 |
9| 10 | 9.4713 | 8.9826 | 8.5302 | 8.1109 | 7.7217 | 7.3601 |
10| 15 | 13.8651 | 12.8493 | 11.9380 | 11.1184 | 10.3797 | 9.7123 |
11| 20 | 18.0456 | 16.3514 | 14.8775 | 13.5903 | 12.4622 | 11.4699 |
12| 25 | 22.0232 | 19.5235 | 17.4132 | 15.6221 | 14.0939 | 12.7834 |
By multiplying 12.7834 (table factor for a 6% rate over 25 years) by the $50,000 payment amount, the result is $639,170—a close reflection of the $639,168 result obtained from the annuity formula, with slight variances due to rounding.
Separate tables also exist for annuities due, offering the correct factors in line with the modified formula.
What Is an Annuity Table Used For?
Annuity tables primarily assist accounting, insurance, and financial professionals to determine an annuity’s present value. They consider the contributed amount and the duration to decide payouts for the annuitant.
Difference Between an Ordinary Annuity and an Annuity Due
- Ordinary Annuity: Payments are made at the end of each period.
- Annuity Due: Payments are made at the beginning of each period.
Can a Lottery Winner Use an Annuity Table?
A lottery winner can indeed use an annuity table to decide whether to take winnings as a lump-sum amount today or as a structured series of payments over years. This form of payout, however, is rarer than investment-related annuities designed to provide a stable retirement income.
Related Terms: present value, discount rate, time value of money, ordinary annuity, annuity due.
