Use this annuity calculator to value ordinary annuities and annuity due payment streams, solve for present value, future value, or required payment.
Display currency
Switch the display currency used for annuity payments, target values, and lump-sum equivalents before entering money amounts.
Solve for
Scenario presets
Start from a common annuity calculator workflow, then adjust the payment, rate, timing, and term.
Annuity type
Future value of annuity calculator
Use Future value mode above to estimate how a regular payment stream could accumulate into a later lump sum.
Present value of annuity calculator
Use Present value mode above to discount future annuity payments to a lump-sum value today and review the PVIFA factor.
Result
Future value of the selected ordinary annuity if the payment stream continues for 15 years.
Annuity assumptions
Effective annual rate: 5.12%. PVIFA factor: 126.46. Future-value annuity factor: 267.29. Annuity due assumes each payment arrives one period earlier than an ordinary annuity, which increases both present and future value.
Ordinary annuity vs annuity due snapshot
This comparison keeps your rate, term, frequency, and solve mode fixed so you can see the timing effect before switching the main scenario.
Beginning-of-period payments usually create a higher present value or future value because each cash flow arrives one period earlier.
Accumulation chart
Year-by-year accumulation
| Year | Balance | Payments | Growth |
|---|---|---|---|
| 1 | $12,278.86 | $12,000.00 | $278.86 |
| 2 | $25,185.92 | $24,000.00 | $1,185.92 |
| 3 | $38,753.34 | $36,000.00 | $2,753.34 |
| 4 | $53,014.89 | $48,000.00 | $5,014.89 |
| 5 | $68,006.08 | $60,000.00 | $8,006.08 |
| 6 | $83,764.26 | $72,000.00 | $11,764.26 |
| 7 | $100,328.65 | $84,000.00 | $16,328.65 |
| 8 | $117,740.51 | $96,000.00 | $21,740.51 |
| 9 | $136,043.20 | $108,000.00 | $28,043.20 |
| 10 | $155,282.28 | $120,000.00 | $35,282.28 |
| 11 | $175,505.67 | $132,000.00 | $43,505.67 |
| 12 | $196,763.73 | $144,000.00 | $52,763.73 |
| 13 | $219,109.39 | $156,000.00 | $63,109.39 |
| 14 | $242,598.30 | $168,000.00 | $74,598.30 |
| 15 | $267,288.94 | $180,000.00 | $87,288.94 |
How to use this result
Use the annuity value to compare a regular payment stream with a lump sum under one steady-rate model. It does not account for inflation-linked payments, taxes, fees, or changing returns unless you model those separately.
Specialized annuity tools
Use these sections for the narrower annuity searches that used to live on separate pages. The level-payment calculator above handles ordinary annuity, annuity due, present value, future value, and required payment amount; the sections below preserve the payout schedule, immediate annuity, deferred annuity, growing annuity, PVIFA, and perpetuity workflows.
Work backward from a lump sum to estimate fixed-term annuity payout income and a year-by-year payout schedule.
Payout frequency
Payment timing
Switch between end-of-period and beginning-of-period withdrawals to match the payout timing you are reviewing. If you are comparing an insurer quote, also check whether the contract is life-contingent, guaranteed for a minimum period, inflation-linked, or paired with survivor benefits, because those features change the real payout.
Estimate single-premium immediate annuity income, payout frequency comparisons, and premium-recovery timing.
Scope note
This page estimates a level term-certain payout from the entered premium and rate assumption. It is a planning worksheet, not an insurer quote, and it does not price mortality credits, riders, taxes, or product-specific contract terms.
Display currency
Immediate annuity products vary by jurisdiction and insurer, but you can still switch the display currency for planning comparisons.
Model premium growth during the deferral period, then convert the accumulated value into payout income.
Deferred annuity
Enter the premium, a steady credited rate, how long income is deferred, how long the payout lasts, and how often payments are made.
Calculate present value, future value, or required first payment when annuity payments rise at a steady growth rate.
Solve for
Annuity type
Display currency
Use your preferred display currency for the first payment, target value, and projected lump-sum equivalents.
Result
Present value of the selected end-of-period annuity whose payments rise at a steady annual growth rate.
Growth impact versus level payments
This separates the value created by the payment growth assumption from the value of making the same first payment every period.
| Scenario | Present value | Future value |
|---|---|---|
| Same first payment, no growth | $128,982.51 | $520,926.66 |
| Added by payment growth | $35,197.10 | $142,151.89 |
Payment milestones
The first, midpoint, and final payments show how the rising-payment schedule changes over the term.
| Milestone | Payment period | Payment amount |
|---|---|---|
| First payment | 1 | $1,000.00 |
| Midpoint payment | 120 | $1,340.61 |
| Final payment | 240 | $1,801.67 |
Rate translation
The calculator converts the selected annual return into an effective rate of 0.58% per payment period and converts the annual payment growth assumption into 0.25% per payment period.
Interpretation
Nominal payments over the full term sum to $326,854.44. Under the current assumptions, that stream compounds into $663,078.55, which is $336,224.10 above the nominal cash contributed.
The present value estimate is $164,179.60, so the discount from the nominal payment total is $162,674.84. If you switch to annuity due, each payment is moved one period earlier and the value rises accordingly.
Assumptions
Effective annual return: 7.23%. Effective annual payment growth: 3%. Total payment periods: 240.
This is a clean mathematical growing-annuity model. It does not adjust for taxes, inflation-linked step-ups that happen only once per year, sequence-of-returns risk, or product-specific retirement rules.
Calculate the present value interest factor of annuity, compare ordinary annuity and annuity due factors, and multiply the factor by a payment amount.
Match the period units
The rate must match the payment period. For example, monthly payments need a monthly discount rate, not an annual rate.
Result
Ordinary annuity factor at 5% per period over 10 periods.
Formula check
PVIFA = (1 - (1 + r)-n) / r. Multiply the factor by the periodic payment amount to get the present value of an annuity.
If the rate is zero, PVIFA collapses to the number of periods. For annuity due timing, the ordinary factor is multiplied by 1 + r because each payment arrives one period earlier.
These rows keep the number of periods fixed while moving the rate by one percentage point. Use them as a quick check before relying on a single annuity factor.
| Scenario | Rate | Ordinary PVIFA | Annuity due PVIFA | Selected PV | Reading |
|---|---|---|---|---|---|
| Lower rate | 4% | 8.1109 | 8.4353 | $8,110.90 | Lower discount rates make the same payment stream worth more today. |
| Base case | 5% | 7.7217 | 8.1078 | $7,721.73 | This row matches the calculator inputs above. |
| Higher rate | 6% | 7.3601 | 7.8017 | $7,360.09 | Higher discount rates reduce PVIFA because later payments are discounted more heavily. |
Value an infinite annuity-style cash flow with level perpetuity and growing perpetuity formulas.
Result
Present value of a growing perpetuity paying $10,000.00 per period.
Income Stream Maths
An annuity calculator estimates the present value or future value of a level payment stream over time. This page also explains the main assumptions behind the annuity calculator result, highlights the supporting figures shown by the calculator, and helps the reader use the estimate without overstating what a quick online tool can prove.
An annuity is a stream of equal payments made at regular intervals. The two most common questions are what that stream is worth today as a lump sum and what it could accumulate to by the end of the term if payments continue and compound.
That is why this calculator offers both present-value and future-value modes. One answers the lump-sum-equivalent question, while the other answers the accumulation question from the same payment stream.
An ordinary annuity assumes each payment arrives at the end of the period. An annuity due assumes each payment arrives at the beginning. Because the money arrives earlier in an annuity due, both present value and future value are higher than for an otherwise identical ordinary annuity.
This timing difference matters in real planning. Rent, insurance premiums, and some retirement-income scenarios are often beginning-of-period cash flows, while loan-style or pension-style schedules are often end-of-period cash flows.
FV of ordinary annuity = PMT x (((1 + i)^n - 1) / i)
Compounds equal end-of-period payments PMT over n periods at periodic rate i.
PV of ordinary annuity = PMT x (1 - (1 + i)^(-n)) / i
Discounts equal end-of-period payments back to a lump-sum present value.
Annuity due value = Ordinary annuity value x (1 + i)
Raises both present and future value when each payment arrives one period earlier.
Suppose a payment stream is 1,000 each month for 15 years at a 5% annual rate with monthly compounding. In future-value mode, the calculator estimates what that stream could accumulate to by the end of the term. In present-value mode, it estimates the lump sum today that would be financially equivalent under the same assumptions.
Switching from ordinary annuity to annuity due lifts both values because every payment gets one extra period of growth or one less period of discounting. That is why payment timing should not be treated as a minor detail when you are comparing cash-flow options.
This calculator assumes a level payment amount and one constant annual rate for the whole schedule. It does not model inflation-linked payments, insurer pricing, mortality credits, surrender charges, taxes, changing yields, or irregular income streams.
Use it as a clean educational annuity model. If you are reviewing a specific product, pension option, or settlement offer, compare this estimate with the official disclosure materials and independent professional advice.
Further reading
The main annuity calculator can now run in four directions: solve for future value, solve for present value, solve for the payment needed to support a target present value, or solve for the regular payment needed to reach a target future value. That preserves the common future value of annuity calculator and present value of annuity calculator workflows without forcing users to decide between several overlapping pages.
The PVIFA factor shown in the result is the present-value multiplier for a one-unit payment stream. The future-value factor plays the same role for accumulation. Together, they make it easier to audit the formula behind the headline result and to compare ordinary annuity timing with annuity due timing.
Required PMT for target PV = Target PV / annuity present-value factor
Solves the regular payment that supports a target lump-sum present value under the selected rate, term, frequency, and payment timing.
Required PMT for target FV = Target FV / annuity future-value factor
Solves the regular payment that accumulates to a target future value under the same annuity assumptions.
The calculator now includes scenario presets for monthly retirement savings, pension-stream valuation, and target future value planning. These presets are not recommendations; they are realistic starting points that expose the key levers: payment amount, target value, annual rate, term, compounding frequency, payment frequency, and whether payments happen at the beginning or end of each period.
The ordinary annuity versus annuity due snapshot is useful because timing is easy to overlook. Competitor annuity calculators often ask users to choose beginning or end payments, but they do not always show the side-by-side effect. Keeping both timing results visible helps you see whether the difference is minor or material before comparing a lump sum, future value target, fixed-term payout, or pension-style income stream.
For product decisions, keep the workflow separate from the quote. Use the calculator to understand the time-value-of-money mechanics, then compare the result with actual annuity contract disclosures, payout-option language, surrender terms, fee schedules, tax treatment, and independent financial advice.
The annuity payout calculator section works backward from a lump sum to estimate fixed-term income, total payout, interest earned, and a year-by-year balance schedule. It is useful for period-certain planning, but it is still not the same as an insurer life-annuity quote because it does not price mortality credits, guarantees, rider costs, or product-specific fees.
The immediate annuity calculator section starts payments right away from a single premium. The deferred annuity calculator section first compounds the premium through an accumulation phase, then converts the later balance into payout income. Keeping both sections together makes the deferred annuity versus immediate annuity trade-off visible without creating separate canonical URLs for the same annuity decision.
A growing annuity differs from a level annuity because each payment rises at a steady growth rate. The growing annuity section calculates present value, future value, or required starting payment while keeping the return assumption separate from the payment-growth assumption.
PVIFA is the present value interest factor of an annuity. It is the factor version of the present-value calculation, useful when you want the multiplier, a sensitivity table, or a quick bridge from payment amount to present value. A perpetuity extends the idea beyond a finite annuity term by valuing a cash flow that continues indefinitely, including the growing perpetuity case when the discount rate is greater than the growth rate.
Growing perpetuity PV = C / (r - g)
Values an infinite growing cash flow when the discount rate r is greater than the growth rate g.
Use the main ordinary-annuity and annuity-due controls when you know the payment amount and need present value or future value. Use the payment-for-target modes when the question is how large each regular payment must be. Use the payout schedule section when you know the lump sum and want income over a fixed term.
Use immediate annuity for income that starts now, deferred annuity for income that starts after an accumulation period, growing annuity for rising payments, PVIFA for a factor/table style calculation, and perpetuity for an infinite-term valuation. Each section uses simplified time-value-of-money math, so product selection, taxes, guarantees, and suitability still require separate review.
Frequently asked questions
Present value estimates the lump sum today that is financially equivalent to the future payment stream. Future value estimates what the payment stream could grow to by the end of the term if it compounds at the chosen rate.
Because each payment arrives one period earlier. Earlier cash flows either compound for longer in future-value mode or are discounted for fewer periods in present-value mode, so the value rises.
Yes, as a first-pass educational estimate for level payment streams. But retirement products and pension options often involve inflation adjustments, fees, survivor benefits, taxes, or insurer assumptions that this simplified model does not include.
Yes for steady-growth payment streams: use the growing annuity section when payments rise at a constant growth rate. It still does not model irregular, contract-specific, inflation-indexed, or manually varying cash flows; those need a more detailed discounted-cash-flow model.
Yes for the fixed-term payout math. Use the payout schedule section when you know the lump sum, rate assumption, payout term, frequency, and beginning-or-end payment timing. It estimates period-certain income and a balance schedule, but it is not an insurer life-annuity quote.
Future value is the default mode in the main calculator. It estimates how equal recurring payments could accumulate over the selected term and keeps the accumulation chart and year-by-year schedule on the canonical annuity page.
Present value is one of the main solve modes. It discounts a level future payment stream to a lump-sum equivalent and shows the PVIFA factor behind the result.
The immediate annuity section assumes payments start right away from the premium. The deferred annuity section first grows the premium through a waiting period, then converts the accumulated value into payout income.
Use growing annuity when the payments rise at a steady growth rate, such as inflation-linked income goals, rising contributions, or stepped cash-flow estimates. Use the standard annuity mode when payments stay level.
PVIFA is the factor used in the present-value annuity formula. Multiplying PVIFA by the periodic payment gives the present value of the annuity stream, assuming the rate, periods, and timing match.
A perpetuity is like an annuity with no fixed ending period. A regular annuity has a finite term, while a perpetuity assumes payments continue indefinitely, so the formula and risk interpretation are different.
Payment timing changes the value of the same cash-flow stream. An annuity due pays at the beginning of each period, so each payment has one extra period to grow in future-value mode or one less period to discount in present-value mode. The snapshot keeps the other assumptions fixed so the timing effect is visible.
No. They are example workflows designed to make the calculator faster to use. Replace the payment, rate, term, frequency, and timing assumptions with your own scenario before relying on the result.
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