# PVIFA Calculator

Created by Bogna Szyk and Tibor Pál, PhD candidate
Reviewed by Dominik Czernia, PhD and Jack Bowater
Based on research by
Dupacova, J.; Hurt J.; Stepa J. Stochastic Modeling in Economics and Finance (2002)
Last updated: Jun 05, 2023

If you have a choice between a massive sum of money or an annuity, and you're not sure which one to pick, this PVIFA calculator is your new best friend. In this article, we will use simple examples to show you what PVIFA is and how you can utilize it in investment decisions. We will also provide you with a small PVIFA table for quick reference.

## 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:

$\mathrm{PVIFA} = \frac{1 - (1+r)^{-n}}{r}$

where:

• $\mathrm{PVIFA}$ – 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? 🙋 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. 1. Determine the number of periods and interest rate. In this case, we have $n = 8$, and $r = 4% = 0.04$. 2. Calculate PVIFA according to the PVIFA formula: $\small \qquad \begin{split} \mathrm{PVIFA} &= \frac{1 - (1+r)^{-n}}{r}\\[1em] &= \frac{1 - (1+0.04)^{-8}}{0.04}\\[1em] &= 6.73 \end{split}$ 1. Now we know that every$1 you receive is, on average, worth 6.73 times more in present value – that is, $6.73. 2. How much is the payment worth, then? The total value of these eight payments will not be equal to simply $8 \cdot \3,\!000$. Instead, we have to multiply the payment value by the PVIFA: $6.73 \cdot \3,\!000 = \20,\!198$ 3. The present value of this annuity is equal to$20,198.

If you want to calculate the present value of the annuity, make sure to open the advanced mode of the PVIFA calculator!

## 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!

Periods ↓ / Interest 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

## FAQ

### How do I calculate PVIFA?

To calculate PVIFA (present value interest factor of annuity), you can use these simple steps:

1. Sum 1 and the decimal interest rate r per period.

2. Elevate the result to the -nth power, where n is the number of compound periods.

3. Subtract the result of point 2. from 1.

4. Divide by r.

The result is the PVIFA, how much the value of your money will increase in the given time, with the given interest.

### What does the PVIFA calculate?

The PVIFA, or present value interest factor of annuity, is a measure of how much value your money will acquire in the case of a long-term investment.

To calculate the PVIFA, you must know the interest rate for a given period of time and the number of these periods you are interested in. The PVIFA tells you, generally, that x money today, if invested, will have a greater value after a given period of time and gives you a quantitative measure of this increase.

### 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 2.723. To calculate this result:

1. Find the decimal interest rate:

5% = 0.05

2. Calculate the following operation:

(1 + r)-n = (1 + 0.05)-3 = 0.863837.

3. Subtract this result from 1:

1 - (1 + r)-n = 1 - 0.864 = 0.136163.

4. Divide the result by r:

(1 - (1 + r)-n)/r = 0.163136/0.050 = 2.723.

This result tells you that your investment today will grow more than two and a half times in three years from now.

### What is the difference between PVIFA and FVIFA?

PVIFA and FVIFA are reciprocal: the present value interest factor of an annuity tells you how much your investment will grow in value, while the future value interest factor of an annuity tells you how much the past one was smaller. Notice that we are not interested in a lump sum but rather a generic change in both cases.

Mathematically speaking, PVIFA and FVIFA are in the following relationship:

PVIFA = 1/FVIFA

Bogna Szyk and Tibor Pál, PhD candidate Interest rate per period (r)
%
Number of periods (n)
PVIFA
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