# Understanding PVIFA: Calculating Present Value of Annuities

![Present Value Interest Factor of Annuity (PVIFA): A factor that can be used to calculate the present value of a series of annuities.](https://www.investopedia.com/thmb/J8WOZ3nBPJswMffgsG1ph5Ar5MA=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/pvifa.asp_FINAL-b83a6fb569444fc28d9d478c1335ce00.png)

*— Investopedia / Hilary Allison*

## What Is the Present Value Interest Factor of Annuity (PVIFA)?

The present value interest factor of an annuity (PVIFA) is a calculation that can help an investor entering into an annuity contract to determine whether it is more advantageous to take a lump-sum payment or to accept a series of payments over time.  

The present value interest factor of an [annuity](https://www.investopedia.com/terms/a/annuity.asp) is used to calculate the [present value of a series of annuities](https://www.investopedia.com/terms/p/present-value-annuity.asp) when it is multiplied by the recurring payment amount. The initial deposit earns interest at the interest rate (r), which perfectly finances a series of (n) consecutive withdrawals and may be written as the following formula:

*   PVIFA = (1 - (1 + r)^-n) / r

PVIFA is also used to calculate the present value of an [ordinary annuity](https://www.investopedia.com/terms/o/ordinaryannuity.asp). The calculation relies on the time value of money. Here we provide some tools and insights to help you utilize PVIFA effectively.

### Key Takeaways

*   The present value interest factor of annuity (PVIFA) helps compare a lump sum payment to annuity payments over time.
*   PVIFA is calculated using the formula: (1 - (1 + r)^-n) / r, where r is the interest rate and n is the number of payments.
*   The time value of money principle implies that money today is worth more than the same amount in the future.
*   Online PVIFA calculators and tables can help estimate present value factors for different interest rates and periods.
*   An annuity due, where payments are made at the beginning of periods, requires adjusting the PVIFA calculation by multiplying by (1+r).

#### Present Value Interest Factor of Annuity (PVIFA)

> **Important**
>
> An annuity factor is a multiplier used to calculate the total payment over the term of an annuity. The annuity factor includes the interest rate, number of payments, and total payment. This calculation shows how interest growth affects your fund over time.

## How the Present Value Interest Factor Works

The present value interest factor is based on the concept of the [time value of money](https://www.investopedia.com/articles/03/082703.asp#:~:text=The%20time%20value%20of%20money%20is%20a%20financial%20concept%20that,the%20same%20amount%20of%20money.), which states that a sum of money today has greater value than the same sum of money at a future date due to its earnings potential.

The present value interest factor helps you decide between taking a lump sum now or an [annuity payment](https://www.investopedia.com/investing/overview-of-annuities/) later. Using estimated rates of return, you can compare the value of the annuity payments to the lump sum.

The present value interest factor may only be calculated if the annuity payments are for a predetermined amount spanning a predetermined range of time.

### Top Tools for Calculating PVIFA

Online tools are available to estimate PVIFA. You can use either of the following:

*   A PVIFA calculator, which determines PVIFA for any combination of entries for an interest rate (r), and a number of payments (n)
*   A PVIFA table, which displays the most common interest rates and number of payments.

The main drawback of a present value interest factor table is that rounding calculated figures reduces precision.  

### Role of the Discount Rate in PVIFA Calculation

The [discount rate](https://www.investopedia.com/terms/d/discountrate.asp) in PVIFA calculations estimates the expected [rate of return](https://www.investopedia.com/terms/r/rateofreturn.asp) for future periods. It is adjusted for risk based on the duration of the annuity payments and the investment vehicle utilized. Higher interest rates result in lower [net present value](https://www.investopedia.com/terms/n/npv.asp) calculations. This happens because a higher anticipated return means $1 today is worth less.

### Calculating the PVIFA for an Annuity Due

When annuity payments are due at the start of a period, they are called an [annuity due](https://www.investopedia.com/terms/a/annuitydue.asp). To calculate the present value interest factor of an annuity due, take the calculation of the present value interest factor and multiply it by (1+r), with "r" being the discount rate.

## How Do You Calculate Present Value Interest Factor for an Annuity?

The formula to calculate PVIFA is (1 - (1 + r)^-n) / r, where r represents the period rate, and n represents the number of payments or withdrawals.

## What Is the Present Value Interest Factor of an Annuity Table?

It is a simple table that features the PVIFAs of common combinations of rates and terms. For example, each column might feature a different rate while each row features a different term. The corresponding cell for each rate/term is the PVIFA.

## What Is the Relationship Between PVIF and PVIFA?

The present value interest factor ([PVIF](https://www.investopedia.com/terms/p/pvif.asp)) formula is used to calculate the current worth of a lump sum to be received at a future date.

The present value interest factor of annuity (PVIFA) is used to calculate the present value of a series of annuity payments.

## The Bottom Line

Calculating the present value interest factor of an annuity (PVIFA) plays an important role in comparing lump-sum payments to annuity payments over time. Understanding the time value of money underscores why a current sum of money is more valuable than the same amount received in the future due to its potential earning capacity.

The formula for PVIFA uses the interest rate and number of payment periods to assess the value of annuity payments. It helps make informed financial decisions regarding annuity contracts and payments. Calculations can be made using online tools and PVIFA tables, but tables are sometimes limited due to rounding errors.

> **Article Sources**
>
> 1.  Omni Calculator. "[PVIFA Calculator](https://www.omnicalculator.com/finance/pvifa)."