Present Value Interest Factor of Annuity (PVIFA) Formula, Tables

The present value interest factor of an annuity is a factor that can be used to calculate the present value of a series of annuities 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 a variable used when calculating the present value of an ordinary annuity.

Understanding Present Value Interest Factor of Annuity

The calculation of PVIFA is based on the concept of the time value of money. This idea stipulates that the value of currency received today is worth more than the value of currency received at a future date. This is because the currency received today may be invested and can be used to generate interest.

Present Value Interest Factor of an Annuity, With Tables

The most common values of both n and r can be found in a PVIFA table, which immediately shows the value of PVIFA. This table is a particularly useful tool for comparing different scenarios with variable n and r values. The rate is displayed across the table's top row, while the first column shows the number of periods.

The cell in the PVIFA table that corresponds to the appropriate row and column indicates the present value factor. This factor is multiplied against the dollar amount of the recurring payment (annuity payment) in question to arrive at the present value.

The Usefulness of the Present Value Interest Factor of Annuity

The present value interest factor of an annuity is useful when determining whether to take a lump-sum payment now or accept an annuity payment in future periods. 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.

Using the Discount Rate for the Present Value Interest Factor

The discount rate used in the present value interest factor calculation approximates the expected rate of return 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 calculations. This is because the value of $1 today is diminished if high returns are anticipated in the future.

Present Value Interest Factor of Annuity Due

If annuity payments are due at the beginning of the period, the payments are referred to as an annuity due. 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.

Frequently Asked Questions

The Bottom Line

The present value interest factor of an annuity provides a useful way to determine if a lump-sum payment now is a better option than future annuity payments. Tables exist to help determine the PVIFA depending on variable factors such as rates and number of payments or withdrawals. A precise factor can be calculated using the formula.