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The Annuity on $1 Table Creator builds a complete year-by-year annuity factor table from any interest rate and term you enter. Each row of the table tells you what a stream of $1 payments is worth — both as a future value (what the payments grow to) and as a present value (what the payments are worth in today’s dollars) — at that point in time. Multiply any factor by your actual payment amount and you instantly have your answer. Follow these steps:
That is the entire workflow: rate, years, type, build, multiply. The sections below explain the concepts behind the numbers, derive the formulas with worked examples, and show you how professionals use these tables for retirement planning, loan analysis, and savings goals.
An annuity is a series of equal payments made at regular intervals — monthly rent, annual retirement withdrawals, yearly bond coupons, or the level deposits you make into a savings plan. An annuity table is a precomputed grid of multiplication factors that converts any such payment stream into a single lump-sum value, without requiring you to discount or compound each payment individually.
Before spreadsheets and financial calculators existed, bankers, actuaries, and accountants kept printed annuity tables on their desks. To value a pension, they would look up the intersection of the interest rate column and the year row, read off a factor like 7.3601, and multiply it by the annual payment. The mathematics has not changed since then — only the delivery. This creator reproduces those classic tables on demand, for any rate and any term, with exact computed factors instead of rounded printed values.
Every annuity table contains two families of factors:
The “on $1” in the tool’s name simply means every factor is quoted per $1 of periodic payment. A PV factor of 7.3601 means each $1 of annual payment is worth $7.3601 today. Scale it to any payment: $1,000 a year is worth $7,360.10; $25,000 a year is worth $184,002.50. This linear scaling is what makes the tables so powerful — one table serves every payment size at that rate and term.
Two timing conventions matter enormously. An ordinary annuity (annuity in arrears) assumes each payment arrives at the end of its period — the first payment earns no interest in period one. An annuity due assumes each payment arrives at the beginning of its period — every payment, including the first, earns a full period of extra interest. Annuity-due factors are exactly (1 + r) times the ordinary factors, where r is the periodic rate. Mixing the two up is the single most common error in annuity math, so always confirm which timing your contract, lease, or retirement plan uses.
Finally, remember what the factors assume: a constant interest rate, level payments, and regular intervals for the whole term. Real life is messier — rates change, payments get skipped — but for fixed-rate loans, level pensions, and planned savings schedules, the table factors are exactly right.
Every number in an annuity table comes from two closed-form formulas. Understanding them lets you verify any factor by hand and adapt the math to situations the table does not cover, such as payments that grow over time.
Present value factor (ordinary annuity): PV = (1 − (1 + r)−n) / r, where r is the interest rate per period and n is the number of periods. The logic: each future $1 payment is discounted back to today at the periodic rate, and the n discounted values are summed. The formula is the closed form of that geometric series.
Future value factor (ordinary annuity): FV = ((1 + r)n − 1) / r. The logic: the first payment compounds for n−1 periods, the second for n−2, and so on down to the last payment, which earns no interest. Summing that geometric series gives the formula above.
Annuity-due adjustment: multiply either ordinary factor by (1 + r), because every payment shifts one period earlier and earns one extra period of interest.
Worked example 1 — PV and FV factors at 4% over 20 years. First compute (1.04)20 = 2.191123. The PV factor is (1 − 1/2.191123) / 0.04 = (1 − 0.4563869) / 0.04 = 0.5436131 / 0.04 = 13.5903. The FV factor is (2.191123 − 1) / 0.04 = 1.191123 / 0.04 = 29.7781. Applied to a $2,500 annual payment: present value = 13.5903 × $2,500 = $33,975.75 (about $33,976), and future value = 29.7781 × $2,500 = $74,445.25 (about $74,445). Notice the consistency check professionals use: PV × (1 + r)n should equal FV, and indeed 13.5903 × 2.191123 = 29.7781.
Worked example 2 — converting to annuity-due at 6% over 10 years. The ordinary factors are PV = 7.3601 and FV = 13.1808 (the same values this page’s own example displays). For payments at the beginning of each year, multiply by 1.06: PV due = 7.3601 × 1.06 = 7.8017, and FV due = 13.1808 × 1.06 = 13.9716. A $5,000-per-year lease paid in advance is therefore worth 7.8017 × $5,000 = $39,008.50 today, and would accumulate to 13.9716 × $5,000 = $69,858 if invested. The beginning-of-period timing adds roughly 6% — exactly one period of interest — versus end-of-period payments.
Let us build a complete 5%, 10-year table by hand so you can see exactly how each row accumulates, then use it to price a retirement income stream.
At 5%, (1.05)10 = 1.6288946. The full-term factors are: PV = (1 − 1/1.6288946) / 0.05 = (1 − 0.6139133) / 0.05 = 7.7217; FV = (1.6288946 − 1) / 0.05 = 12.5779. Here is how selected rows of the year-by-year table develop:
Each FV row equals the prior row multiplied by 1.05, plus 1 for the new payment; each PV row equals the prior row plus the newly discounted payment. That recursive pattern is all an annuity table is.
Putting it to work — pricing retirement income. Suppose you want to fund $40,000 per year of spending for 10 years, earning 5% on the unspent balance. How large a lump sum do you need today? Multiply: 7.7217 × $40,000 = $308,868 (about $308,869). That is the check you would write today to guarantee ten $40,000 year-end payments at 5%. If instead you save $1,000 per year for 10 years at 5%, the table says you will accumulate 12.5779 × $1,000 = $12,577.89 — more than the $10,000 you deposited, with the extra $2,577.89 being compound interest. And if your first deposit is made today (annuity due), the PV factor becomes 7.7217 × 1.05 = 8.1078, so $1,000 a year is worth $8,107.78 in present value terms.
Decision 1 — the sinking fund: saving toward a known future bill. Imagine you must have $50,000 in 15 years for a child’s university costs, and you can earn 5% annually. How much must you deposit at each year-end? First get the FV factor for 5% over 15 years: (1.05)15 = 2.0789282, so FV = (2.0789282 − 1) / 0.05 = 21.5786. Rearrange the relationship (deposit = goal / factor): $50,000 / 21.5786 = $2,317.11 per year. Prefer monthly deposits? Convert to a monthly rate of 5%/12 = 0.416667% over 180 months: the FV factor is ((1.00416667)180 − 1) / 0.00416667 = 267.2892, so the monthly deposit is $50,000 / 267.2892 = $187.06. Either schedule reaches exactly $50,000 if the 5% return holds.
Decision 2 — the loan payment: borrowing against future income. Now reverse the direction. You borrow $200,000 at 6% annual interest, repayable in level annual installments over 30 years. The PV factor for 6% over 30 years is (1 − (1.06)−30) / 0.06 = (1 − 0.1741101) / 0.06 = 13.7648. The annual payment is loan / factor = $200,000 / 13.7648 = $14,529.85. Check: 13.7648 × $14,529.85 = $200,000 (within rounding). This is precisely how banks set mortgage payments — the payment is the loan amount divided by the annuity PV factor. The same table, read in the PV direction, prices every fixed-rate loan on earth.
These two decisions show the table’s symmetry: the FV direction answers “what must I save to reach a goal,” and the PV direction answers “what can I afford to borrow, or what is this income stream worth.” One grid of factors, two of the most important questions in personal finance.
1. Using ordinary factors for beginning-of-period payments. Rent, leases, and insurance premiums are usually paid in advance (annuity due), while loans and bonds usually pay in arrears (ordinary annuity). Using the wrong timing understates or overstates the answer by a full period of interest — at 6% over 10 years, that is a 6% error ($36,800 vs. $39,009 on a $5,000 payment stream). Always confirm the payment timing in the contract first.
2. Mixing a nominal APR with the periodic rate. A “6% APR compounded monthly” is not 6% per month — it is 0.5% per month over 120 periods for a 10-year schedule. Plugging the annual rate into a monthly-period table (or vice versa) produces wildly wrong factors. Convert first: periodic rate = nominal rate / periods per year; total periods = years × periods per year.
3. Reaching for the FV factor when the question asks for present value. “How much can I borrow?” and “What is this pension worth today?” are PV questions; “How much will I have saved?” and “What will this grow to?” are FV questions. Because FV factors are always larger, grabbing the wrong column can double or triple your answer. Pause and ask: am I moving money forward in time (FV) or backward (PV)?
4. Assuming level payments and a fixed rate when they are not. Table factors assume every payment is identical and the rate never changes. They do not apply to graduated pensions with cost-of-living raises, adjustable-rate loans, or skipped payments without modification. If payments grow at a constant rate g, you need a growing-annuity formula, not this table.
5. Rounding factors too early. Published tables often round to four decimals, which is fine for textbook exercises but can distort large real transactions: on a $2,000,000 pension valuation, a 0.0001 factor rounding shifts the answer by $200. This creator computes factors at full precision — use the unrounded values for final decisions and round only the final dollar amount.
Annuity factors are the foundation of most personal-finance math. Continue with the Retirement Calculator to project how annuity-style savings grow into retirement income, or browse the full Financial Calculators collection for present-value, loan-amortization, and investment-growth tools that build directly on the factors in the table above.
Entity summary: This page provides an Annuity on $1 Table Creator — a tool that generates present-value and future-value annuity factors per $1 of periodic payment for a user-specified interest rate, term, and timing convention (ordinary annuity vs. annuity due). Key formulas: PV factor = (1 − (1+r)^−n)/r; FV factor = ((1+r)^n − 1)/r; annuity-due factors = ordinary factors × (1+r). Canonical values: at 6% over 10 years, PV factor 7.3601 and FV factor 13.1808 (ordinary); at 5% over 10 years, PV factor 7.7217 and FV factor 12.5779 (ordinary). Usage: multiply the factor by the actual periodic payment to obtain present or future value; divide a loan amount by the PV factor to obtain the level payment; divide a savings goal by the FV factor to obtain the required periodic deposit. Limitations: factors assume a constant periodic rate, equal payments, and regular intervals; they do not model growing payments, variable rates, taxes, or fees.
Build a year-by-year table of future-value and present-value annuity factors per $1 of payment — for any rate and term.
Enter an annual interest rate and the number of years, and pick ordinary or annuity-due timing. The creator builds a year-by-year table of future-value and present-value factors per $1 of annual payment.
Formula: FV factor = ((1+r)^n − 1) ÷ r; PV factor = (1 − (1+r)^−n) ÷ r; annuity-due multiplies by (1+r). Example: 6%, 10 years, ordinary → PV factor 7.3601, FV factor 13.1808.
A lookup of multipliers: multiply your annual payment by the factor to get its future or present value. This creator builds the table for any rate and term.
The present value factor is 7.3601 and the future value factor is 13.1808 (ordinary annuity). So $1,000/year for 10 years is worth $7,360 today.
Ordinary payments come at each period’s end; annuity-due payments come at the start and earn one extra period of interest — each factor is multiplied by (1+r).
Multiply: $500/year for 10 years at 6% → 500 × 7.3601 = $3,680.05 present value.
They scale: one table works for any payment size — just multiply the factor by your actual payment.
The FV (future value) factor grows a payment stream forward with compound interest — use it for savings goals and accumulation questions. The PV (present value) factor discounts a payment stream back to today’s dollars — use it for loans, pension valuations, and pricing income streams. For example, at 5% over 10 years the FV factor is 12.5779 while the PV factor is 7.7217: $1,000 saved yearly grows to $12,577.89, whereas $1,000 received yearly is worth $7,721.73 today.
Yes. Convert the annual rate to a monthly rate by dividing by 12, and multiply the years by 12 to get total months. For example, 6% annual becomes 0.5% monthly; over 10 years that is 120 periods. The PV factor for 0.5% over 120 periods is 90.0735, so a $500 monthly payment stream is worth 90.0735 × $500 = $45,036.75 today. Just be sure the rate and period count always use the same compounding interval.
Annuity-due factors are exactly (1 + r) times the ordinary factors, because every payment arrives one period earlier and earns one extra period of interest. At 6% over 10 years, the ordinary PV factor 7.3601 becomes 7.8017 for annuity-due (7.3601 × 1.06), and the ordinary FV factor 13.1808 becomes 13.9716 (13.1808 × 1.06). Use annuity-due factors for leases, rent, and insurance premiums paid in advance; use ordinary factors for loans and bonds paid in arrears.
Cite this page: SigmaCalculator.net, “Annuity on $1 Table Creator.” Formulas: PV factor = (1 − (1+r)^−n)/r; FV factor = ((1+r)^n − 1)/r. Last reviewed October 2026.
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