When you save the same amount every period, the future value of annuity factor tells you how big the pile will be. Tables of these factors are a staple of accounting and finance courses, CFA and CPA study, and engineering-economics exams, and they are handy for quick planning: one lookup and one multiplication. This generator builds the table for ordinary annuities or annuities due over the rates and periods you choose.
How to generate the table
- Choose end of each period (ordinary annuity) or start (annuity due).
- Set the range of interest rates for the columns and the step between them.
- Set the range of periods for the rows.
- Choose the decimal places.
The result above the table reads the bottom-right factor and shows how much of it is interest.
The annuity factor formula
For an annuity due, multiply by (1 + i). The future value of any level payment is then FV = PMT × factor.
Worked example
You will put $2,400 at the end of each year into a college fund earning 5% for 20 years.
- Row 20, column 5%: 33.0660
- Future value: $2,400 × 33.0660 = $79,358.40
- You deposit $48,000 in total, so about $31,358 is interest
If you make each deposit at the start of the year instead, the annuity-due factor is 34.7193 and the fund reaches about $83,326.
Using the table in reverse: sinking funds
The same factor tells you how much to set aside to reach a target. Divide the goal by the factor:
| Goal | Rate | Years | Factor | Yearly deposit |
|---|---|---|---|---|
| $50,000 | 5% | 10 | 12.5779 | $3,975.23 |
| $50,000 | 5% | 20 | 33.0660 | $1,512.13 |
| $50,000 | 7% | 30 | 94.4608 | $529.32 |
Companies use this sinking-fund arithmetic to plan for bond repayments and equipment replacement; households use it for tuition, a new roof or a car. The reciprocal of the factor is the sinking fund factor (A/F), which also appears in the compound interest factor table.
How the factor builds up
Each factor is a running total of future value factors: FVIFA(i, n) = 1 + (1 + i) + (1 + i)2 + … + (1 + i)n−1. At 5%, row 3 is 1 + 1.05 + 1.1025 = 3.1525. Moving one row down adds the next growth factor, so differences between rows match the future value of $1 table.
Matching rates and periods
For monthly deposits, use a monthly rate column (annual rate ÷ 12) and the number of months as the row. With an annual rate of 6% that means a 0.5% column; 10 years of monthly saving is row 120.
For exact answers with any payment and compounding frequency, or with growing payments, use the future value of annuity calculator. To value payments you will receive rather than make, see the present value of annuity table.
Factors are exact values rounded to your chosen decimals. For study and planning; not financial advice.
Frequently asked questions
What does a future value of annuity table show?
Each cell is the future value interest factor of an annuity (FVIFA): what a payment of $1 at the end of each period grows to after n periods at rate i. Multiply by your payment to get the future value of your annuity.
How do I convert an ordinary annuity factor to an annuity due?
Multiply it by (1 + i), or switch the table to 'Start (annuity due)'. At 5% for 20 periods, the ordinary factor 33.0660 becomes 33.0660 × 1.05 = 34.7193.
Why is the factor for one period always 1?
With an ordinary annuity, a single payment made at the end of the only period has no time to earn interest, so $1 is still $1. For an annuity due, the one-period factor is 1 + i.
How do I use the table to plan a sinking fund?
Divide the target amount by the factor. To accumulate $50,000 in 10 years at 5% with year-end deposits, divide $50,000 by 12.5779 to get deposits of about $3,975 a year.
What happens at a 0% rate?
The factor simply equals n, because each $1 deposit stays $1. The gap between the factor and n at any positive rate is the interest earned per dollar of payment.