Generate a custom PVIFA table for ordinary annuities or annuity due. Set your own interest rate range, period range, and increment values to create a printable reference table.
Configure Your PVIFA Table
Interest Rates (Columns)
Maximum 20 columns
First column interest rate
Increase per column
Periods (Rows)
Maximum 50 rows
First row period number
Increase per row
Present Value of an Ordinary Annuity of $1 (PVIFA)
PVOA = (1/i) × [1 – 1/(1+i)^n]
Ordinary Annuity vs Annuity Due
Annuity type determines when payments occur within each period, which directly affects the present value calculation.
Ordinary Annuity
Payments arrive at the end of each period. Most loans, mortgages, and bonds use this structure. Also called an annuity in arrears.
Annuity Due
Payments arrive at the beginning of each period. Rent, insurance premiums, and lease payments often follow this pattern. Also called an annuity in advance.
Because annuity due payments arrive one period earlier, they are discounted less. As a result, PVAD is always greater than PVOA for the same rate and number of periods: PVAD = PVOA × (1 + i).
PVIFA Formulas Explained
Ordinary Annuity (T = 0)
PVOA = (1/i) × [1 − 1/(1+i)^n]
Annuity Due (T = 1)
PVAD = (1/i) × [1 − 1/(1+i)^n] × (1 + i)
In both formulas, i is the interest rate per period as a decimal and n is the number of periods. For payments of $PMT, multiply PVIFA by PMT to get the total present value of the annuity stream.
Example: Payments of $1,000 per year for 5 years at 6% annual interest. PVOA at n=5, i=6% = 4.2124. Total present value = $1,000 × 4.2124 = $4,212.40.
Perpetuity (n approaches infinity)
When n approaches infinity, the formula simplifies to: PVIFA = 1 / i. At 5%, a $1 perpetuity has a present value of $20. At 10%, the present value is $10.
Practical Uses of the PVIFA Table
Loan Payment Analysis
Lenders use PVIFA to calculate the present value of all scheduled loan repayments. If the present value of the payment stream equals the loan principal at the given rate, the payment schedule is correctly priced.
Retirement Planning
If you want to receive $2,000 per month in retirement for 20 years and your portfolio earns 5% annually, the PVIFA table tells you the lump sum you need today to fund that income stream.
Lease Valuation
Accountants use PVIFA to calculate the present value of future lease obligations for balance sheet reporting under accounting standards that require capitalisation of operating leases.
Frequently Asked Questions
Clear answers to common questions about PVIFA tables, annuity types, and present value of annuity calculations.
PVIFA stands for Present Value Interest Factor of an Annuity. It is the factor you multiply by a periodic payment amount to find the total present value of all those payments. The formula for an ordinary annuity is PVIFA = (1 − 1/(1+i)^n) / i, where i is the interest rate per period and n is the number of periods.
An ordinary annuity makes payments at the end of each period. An annuity due makes payments at the beginning of each period. Because annuity due payments arrive one period earlier, each payment is discounted less, so the present value of an annuity due is always higher than an equivalent ordinary annuity. PVAD = PVOA × (1 + i).
Find the row matching your number of periods and the column matching your interest rate. Multiply the factor in that cell by the periodic payment amount. For example, if payments are $500 per year for 5 years at 6%, and PVIFA = 4.2124, the present value is $500 × 4.2124 = $2,106.18.
The PVIFA formula for an ordinary annuity is PVIFA = (1 − 1/(1+i)^n) / i, where i is the interest rate per period as a decimal and n is the number of periods. This formula sums the present value factors for each individual payment in the annuity.
The PVIFA formula for an annuity due is PVAD = ((1 − 1/(1+i)^n) / i) × (1 + i). This is the ordinary annuity PVIFA multiplied by (1 + i), which accounts for each payment arriving one period earlier.
PVIF applies to a single lump sum payment. PVIFA applies to a series of equal periodic payments. PVIFA is the sum of individual PVIF values for each payment period in the annuity.
PVIFA decreases as interest rates rise. A higher interest rate discounts each future payment more heavily, reducing the present value of the entire annuity stream. Conversely, PVIFA increases as interest rates fall, because future payments are discounted less.
A perpetuity is an annuity that pays forever with no end date. As the number of periods approaches infinity, PVIFA approaches 1 / i. At an interest rate of 5%, the present value of a $1 perpetuity is 1 / 0.05 = $20. This means $20 invested today at 5% produces $1 per year forever.
