Present Value of $1 Annuity Table (PVIFA) -

Interest Rate (i) Range

Min Rate (%):

Max Rate (%):

Rate Step (%):

Periods (n) Range

Min Periods:

Max Periods:

Period Step:

Decimal Places for Factors:

Present Value of an Ordinary Annuity of $1 (PVIFA) Table

How to Use the PVIFA Table Generator

Define Interest Rate (i) Range:
- Min Rate (%): Enter the starting interest rate per period (e.g., 1 for 1%).
- Max Rate (%): Enter the ending interest rate per period (e.g., 12 for 12%).
- Rate Step (%): Enter the increment for the interest rates (e.g., 1 to show rates like 1%, 2%, 3%, etc.).
Define Periods (n) Range:
- Min Periods: Enter the starting number of payment periods (e.g., 1).
- Max Periods: Enter the ending number of payment periods (e.g., 25).
- Period Step: Enter the increment for the periods (e.g., 1 for consecutive periods).
Set Decimal Places: Choose the number of decimal places for the PVIFA factors (typically 4 to 6).
Generate Table: Click the “Generate Table” button.
View Table: The Present Value Interest Factor of an Ordinary Annuity (PVIFA) table will be displayed.
- Interest rates (i) are shown across the top row.
- Number of periods (n) are listed in the first column.
- Each cell contains the PVIFA factor for the corresponding ‘i’ and ‘n’, calculated as [1 - (1 + i)^-n] / i. This factor represents the present value of a series of $1 payments made at the end of each period.
Using the Table: To find the present value of an ordinary annuity with payments other than $1, multiply the periodic payment amount by the PVIFA factor found in the table.
Errors: Invalid inputs (e.g., max rate
Clear Table: Click “Clear Table” to remove the generated table.

Valuing Streams of Income: The Present Value of an Annuity (PVIFA) Table

What is an Annuity and Why is its Present Value Important?

Many financial situations involve not just a single future sum, but a series of regular, equal payments over a period of time. This series of payments is known as an annuity. Common examples include mortgage payments, car loan payments, regular contributions to a retirement fund, or income streams from certain investments. Just like a single future sum, a future stream of payments is also worth less today due to the time value of money. The Present Value of an Annuity (PVA) tells us the total current worth of all those future payments combined, discounted back to the present.

A Present Value Interest Factor of an Annuity (PVIFA) table provides pre-calculated factors that simplify finding the PVA for an ordinary annuity where each payment is $1. An ordinary annuity is one where payments are made at the end of each period. This table generator helps you create custom PVIFA tables for your specific needs.

The Formula Behind PVIFA: Summing Discounted Payments

The PVIFA factor essentially sums up the present value interest factors (PVIF) for each individual payment in the annuity stream. The direct formula for PVIFA is:

PVIFA_i,n = [1 - (1 + i)^-n] / i

Where:

PVIFA_i,n = Present Value Interest Factor of an Ordinary Annuity for interest rate ‘i’ and ‘n’ periods.
i = Interest rate (or discount rate) per period (expressed as a decimal).
n = Number of payment periods.

If the interest rate i is 0, the formula simplifies: PVIFA_0,n = n. This makes sense, as with no discounting, the present value of receiving $1 for ‘n’ periods is simply $n.

Each factor in the table tells you what a series of $1 payments, received at the end of each period for ‘n’ periods, is worth today when discounted at rate ‘i’.

Ordinary Annuity vs. Annuity Due

It’s crucial to distinguish between an ordinary annuity (payments at the end of periods) and an annuity due (payments at the beginning of periods). PVIFA tables are typically for ordinary annuities. An annuity due is always worth more in present value terms because each payment is received one period sooner. The factor for an annuity due (PVIFAD) can be found by multiplying the PVIFA factor by (1 + i).

How to Read and Use a PVIFA Table

PVIFA tables are structured similarly to PVIF tables:

Interest Rates (i) are in the top row.
Number of Periods (n) are in the first column.

To use the table:

Find the column for your per-period interest rate.
Find the row for your total number of payment periods.
The PVIFA factor is at the intersection of this row and column.

Calculating Present Value of an Annuity (PVA): Once you have the PVIFA factor, multiply it by the actual periodic payment amount (PMT) to find the PVA:

PVA = PMT × PVIFA_i,n

Example: You are offered an investment that will pay you $500 at the end of each year for 10 years. Your required rate of return (discount rate) is 6% per year. From a PVIFA table (or this generator), PVIFA_{6%, 10 years} is approximately 7.36009.

PVA = $500 × 7.36009 ≈ $3,680.05

This means the series of ten $500 payments is worth approximately $3,680.05 to you today.

Interpreting PVIFA Factors

Observing the trends in a PVIFA table reinforces key financial concepts:

Higher Interest Rates, Lower PVIFA: As the discount rate (i) increases, the PVIFA factor decreases. Higher rates mean future payments are discounted more heavily, reducing their present value.
More Periods, Higher PVIFA (Usually): As the number of periods (n) increases, the PVIFA factor generally increases because you are summing the present values of more payments. However, the incremental increase in PVIFA diminishes as ‘n’ gets very large, especially at higher interest rates, because distant payments contribute very little to the present value.

“An annuity is a stream of fixed payments, but its value today ebbs and flows with the tides of interest rates and time.” – A financial adage. PVIFA tables help chart these ebbs and flows.

Applications: Where is PVIFA Used?

PVIFA calculations are vital in many financial contexts:

Loan Amortization: Determining the principal amount of a loan given a series of equal payments (e.g., mortgages, car loans). The loan amount is the present value of the payment stream.
Bond Valuation: The stream of coupon payments from a bond forms an annuity, and their present value is part of the bond’s price.
Retirement Planning: Calculating how much you can withdraw periodically from a retirement nest egg, or how large a lump sum is needed to fund a desired retirement income stream.
Investment Analysis: Evaluating projects or investments that generate a steady stream of cash flows.
Lease Valuation: Determining the present value of future lease payments.
Legal Settlements: Calculating the lump-sum equivalent of a structured settlement that involves periodic payments.

The Modern Context: Tables vs. Direct Calculation

Like PVIF tables, PVIFA tables were once indispensable for manual calculations. Today, financial calculators and software can compute PVA directly. However, understanding PVIFA tables and the factors they contain provides a solid conceptual foundation for these more complex tools. Generating a PVIFA table can still be a valuable exercise for learning how discount rates and time affect the present value of a stream of payments.

This PVIFA Table Generator empowers you to create tailored tables, allowing for exploration and deeper understanding of annuity valuation. Whether for academic purposes, quick estimations, or reinforcing your financial literacy, it’s a handy tool for anyone dealing with the time value of money.