Calculate the Present Value Interest Factor of an Annuity (PVIFA), based on the time value of money principle. Determines the present value of future annuity payments.
PVIFA Calculator
Calculate the Present Value Interest Factor of an Annuity (PVIFA).
What is PVIFA?
PVIFA is an abbreviation for present value interest factor of annuity. It is an idea based on the time value of money: the money you have now is worth more than the same amount of money a few years from now.
Why is money worth more today?
The reason is simple – you can decide to invest it so that it will generate interest. All that potentially earned money increases the value of the cash you have right now.
Now, imagine you're given a choice: you can either get a considerable sum of money today or regular payments spread over a few years (also called annuity payments). Which option should you choose? It's a tricky question because the future value of annuity is different than the same amount of money today. To answer it, you need to use this PVIFA calculator.
PVIFA formula
Now that we know what PVIFA is and how to use it, let's transform our knowledge into a mathematical equation. The PVIFA formula looks like this:
$$ \text{PVIFA} = \frac{1 - (1 + r)^{-n}}{r} $$where:
- PVIFA – Present value interest factor of annuity;
- r – Interest rate per period, expressed as a decimal; and
- n – Number of periods (years).
If you're interested in some additional knowledge, the interest rate calculator can explain how this quantity is calculated.
Now, we can use this PVIFA formula to figure out what's the future value of eight consecutive payments, obtained once a year at an interest rate of 4% per year. How? Let's take a look at an example below.
How to use the PVIFA calculator? An example
Imagine you have invested in a promising startup that produces 3D printers. Your investment will result in you getting eight payments of $3,000 – one per year. The interest rate, as we mentioned above, is equal to 4%. What is the present value of this annuity?
(Note: In evaluating an annuity, we consider its present and future value. You can learn more about both of them from the present value of annuity calculator and the future value of annuity calculator, respectively.)
- Determine the number of periods and interest rate. In this case, we have n=8, and r=4% (or 0.04 as a decimal).
- Calculate PVIFA using the formula (this is what the calculator above does):
$$ \text{PVIFA} = \frac{1 - (1 + r)^{-n}}{r} = \frac{1 - (1 + 0.04)^{-8}}{0.04} \approx 6.73274 $$
Enter Rate=4% and Periods=8 into the calculator above to get this PVIFA factor.
- Now we know that every $1 received annually for 8 years at 4% is worth approximately $6.73 today.
- Use the PVIFA factor to find the Present Value of the Annuity (this step is done *after* using the calculator):
The total value of these eight payments will not be equal to simply 8 * $3,000. Instead, we have to multiply the payment value by the PVIFA factor: $$ \text{PV of Annuity} = \text{Payment} \times \text{PVIFA} $$ $$ \text{PV of Annuity} = \$3,000 \times 6.73274 \approx \$20,198.23 $$
The present value of this annuity is equal to approximately $20,198.23.
Remember: This calculator finds the PVIFA factor (e.g., 6.73274). You then use that factor with your payment amount to find the total present value.
PVIFA table
Before our handy PVIFA calculator existed, people had to deal with these calculations differently. Instead of using the formula, you could work with a PVIFA table, where you'd find the PVIFA values for most common interest rates and numbers of periods.
The PVIFA table below shows the value of PVIFA for interest rates spanning from 1% to 5% and for 1 to 5 periods. If your investment has a higher rate, or you're planning on getting the annuity for more than five years, make sure to use the PVIFA calculator instead!
(Example Table Description - Actual table not generated here)
| Periods ↓ / Rate → | 1% | 2% | 3% | 4% | 5% |
|---|---|---|---|---|---|
| 1 | 0.9901 | 0.9804 | 0.9709 | 0.9615 | 0.9524 |
| 2 | 1.9704 | 1.9416 | 1.9135 | 1.8861 | 1.8594 |
| 3 | 2.9410 | 2.8839 | 2.8286 | 2.7751 | 2.7232 |
| 4 | 3.9020 | 3.8077 | 3.7171 | 3.6299 | 3.5460 |
| 5 | 4.8534 | 4.7135 | 4.5797 | 4.4518 | 4.3295 |
FAQs
- How do I calculate PVIFA?
- To calculate PVIFA (present value interest factor of annuity), you can use these simple steps:
- Sum 1 and the decimal interest rate r per period.
- Elevate the result to the -nth power, where n is the number of compound periods.
- Subtract the result of point 2. from 1.
- Divide by r.
- What does the PVIFA calculate?
- The PVIFA, or present value interest factor of annuity, is a factor used to calculate the present value of a series of equal future payments (an annuity). It represents the present value of receiving $1 per period for 'n' periods at interest rate 'r'. Multiplying PVIFA by the periodic payment amount gives the total present value of the annuity.
- What is the PVIFA of 3 year investment with interest 5%?
- The PVIFA for a 3-year investment with an annual interest of 5% is approximately 2.7232. To calculate this result:
- Find the decimal interest rate: 5% = 0.05
- Calculate the following operation: (1 + r)-n = (1 + 0.05)-3 ≈ 0.863838
- Subtract this result from 1: 1 - (1 + r)-n = 1 - 0.863838 = 0.136162
- Divide the result by r: (1 - (1 + r)-n)/r = 0.136162 / 0.050 ≈ 2.7232
- What is the difference between PVIFA and FVIFA?
- PVIFA (Present Value Interest Factor of Annuity) helps find the value *today* of a series of future payments. FVIFA (Future Value Interest Factor of Annuity) helps find the value *at the end* of the payment period of a series of payments made over time. PVIFA discounts future payments back to the present, while FVIFA compounds past payments forward to the future.
