Annuity Table for an Ordinary Annuity
An annuity table is a tool that simplifies the calculation of the present value of an annuity. Also referred to as a “present value table,” an annuity table contains the present value interest factor of an annuity (PVIFA), which you then multiply by your recurring payment amount to get the present value of your annuity.
There are many reasons you might want to know the present value of your annuity. Chief among them is the ability to tailor your financial plan to your current financial status. The present value of your annuity is a component of your net worth, and you need this information to ensure a comprehensive picture of your finances.
Just as you regularly review your credit card statements, bank balances and investments, you’ll want to know the value of your annuity at any given point in time. As any expert in financial literacy will attest, your balance sheet is the foundation for everything from your budget to your retirement savings.
So, how do you use an annuity table to calculate the present value of an annuity?
First, you need to know whether you receive your payments at the end of the period — as is the case with an ordinary annuity — or at the beginning of the period. When payments are distributed at the beginning of a period, the annuity is referred to as an annuity due. Annuity due payments typically apply to expenses such as rent or car leases where payments are made on the first of the month.
Because most fixed annuity contracts distribute payments at the end of the period, we’ve used ordinary annuity present value calculations for our examples.
You also need your payment amount and your discount rate. If you don’t know them off-hand, you can find them in your contract.
Present value tables aren’t as precise as manual calculations or financial software programs because the tables contain a limited set of interest rates and payments. If you take a look at a variety of ordinary annuity tables, you’ll see the factors are all within a decimal place, depending on whether they are rounded. Additionally, you can use them only with fixed payment amounts and interest rates.
If this sounds confusing, keep reading. It’s not as complicated as it appears.
What Is an Annuity Table?
An annuity table, or present value table, is simply a tool to help you calculate the present value of your annuity.
Based on the time value of money, the present value of your annuity is not equal to the accumulated value of the contract. This is because the payments you are scheduled to receive at a future date are actually worth less than the same amount in your bank account today.
The time value of money states that a dollar today is worth more than it will be at any point in the future. It makes sense when you consider that every dollar has earning potential because it can be invested with the expectation of a return. So, if you have $1,000 right now, and you put it in a high-yield savings account with a 1 percent annual percentage yield (APY), at the end of a year, you will have $1,010.
Conversely, if I hand you $1,000 in cash at the end of the year, you will have $1,000. So, essentially, the $1,000 I give you 365 days from now is worth only $990 to you because you’ve missed the opportunity to invest it and earn the 1 percent compound interest.
This example is an easy calculation because we’re dealing with simple round numbers and only one payment period. But when you’re calculating multiple payments over time, it can get a bit more complicated.
That’s where an annuity table comes in handy.
What Are the Benefits of Using an Annuity Table?
Although annuity tables are not as precise as annuity calculators or spreadsheets, the benefit of using an annuity table is the ease of calculating the present value of your annuity.
When the payments are fixed, the present value interest factor of an annuity (PVIFA) — these are the values that correspond to the intersection of the number of payments remaining and the interest rate — can be simplified.
An annuity table provides you with the PVIFA by which you will multiply your payment amount to arrive at your annuity’s present value, thus eliminating the need for you to work out the most complicated step in the present value formula.
Present Value of an Annuity Formula
The formula for finding the present value of an ordinary annuity is often presented one of two ways, where “r” represents the interest rate and “n” represents the number of periods.
Using either of the two formulas below will provide you with the same result.
In the PVOA formula, the present value interest factor of an annuity is the part of the equation that is written as and multiplied by the payment amount. Therefore, if you consult an annuity table, you can easily find the PVIFA by identifying the intersection of the number of payments (n) on the vertical axis and the interest rate (r) on the horizontal axis.
Present Value of an Annuity Table
Annuity tables can be helpful for finding the present value of an annuity because they do the mathematical legwork for you.
Below is an example of an annuity table for an ordinary annuity. Remember that all annuity tables contain the same PVIFA factor for a given number of periods at a given rate, just like all times tables contain the same product for any two given numbers. Any variations you find among present value tables for ordinary annuities are due to rounding.
Other Methods for Calculating the Present Value of an Annuity
There are other methods for calculating the present value of an annuity. Each has a different level of effort and required mathematical skill.
- Annuity calculator
- Excel spreadsheet
- Manual Formula
For example, using Excel, you can find the present value of an annuity with values that fall outside the range of those included in an annuity table.
Perhaps you own a fixed annuity that pays a set amount of $10,000 every year. The terms of your contract state that you will hold the annuity for 7 years at a guaranteed effective interest rate of 3.25 percent. You’ve owned the annuity for five years and now have two annual payments left. You can find the exact present value of your remaining payments by using Excel.
Depending upon the numbers you’re working with and how accurate you want to be, an annuity table is a simple and convenient way to calculate the present value of an ordinary annuity.
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