About

An annuity converts a lump-sum PV into a stream of fixed periodic payments over n periods at a guaranteed rate r. Miscalculating the periodic payout PMT by even 0.25% on the rate input can compound into thousands of dollars of unexpected shortfall over a 20-year drawdown. This calculator implements the standard present-value annuity equation used by actuaries and pension administrators. It supports ordinary annuities (end-of-period) and annuities-due (beginning-of-period), optional annual growth adjustments for inflation protection, and generates a full amortization schedule showing interest earned versus principal consumed each period.

The tool assumes a fixed nominal interest rate compounded at the payout frequency. It does not account for taxes, surrender charges, or mortality credits that vary by insurance contract. For inflation-adjusted payouts, use the growth rate field to model a constant annual escalation g. Note: the growing annuity formula breaks down when g = r. Pro tip: compare monthly versus quarterly frequencies. Monthly payouts reduce per-payment amounts but earn slightly less interest per period due to earlier withdrawals.

Formulas

The periodic payout for an ordinary annuity (payments at end of each period) is derived from the present value of an annuity formula:

PMT = PV × r1 − (1 + r)⁻ⁿ

For an annuity-due (payments at beginning of each period), the adjustment is:

PMT_due = PMT_ordinary1 + r

For a growing annuity where each payment increases by a constant rate g per period (and g ≠ r):

PMT₁ = PV × r − g1 − (1 + g1 + r)ⁿ

The periodic interest rate is derived from the nominal annual rate:

r = r_annualm

Total number of periods:

n = t × m

Where PV = present value (lump sum invested), PMT = periodic payout amount, r = periodic interest rate, n = total number of payout periods, m = number of payments per year (12 for monthly, 4 for quarterly, 2 for semi-annual, 1 for annual), t = payout duration in years, g = periodic growth rate for inflation-adjusted payouts, PMT₁ = first payment in a growing annuity series.

Reference Data

Annuity Type	Payment Timing	Typical Use Case	Formula Adjustment
Ordinary Annuity (Immediate)	End of period	Pension payouts, bond coupons	Standard PMT formula
Annuity-Due	Beginning of period	Rent, insurance premiums, lease payments	PMT × (1 + r)
Growing Annuity	End of period (escalating)	Inflation-adjusted retirement income	Uses growth rate g
Perpetuity	End of period (infinite)	Endowments, preferred stock	PMT = PV × r

Payout Frequency	Periods/Year	Rate Divisor	Typical Application
Monthly	12	r ÷ 12	Retirement income, Social Security
Quarterly	4	r ÷ 4	Dividend distributions
Semi-Annual	2	r ÷ 2	Bond interest payments
Annual	1	r	Structured settlements

Lump Sum ($)	Rate (%)	Years	Monthly Payout ($)	Total Received ($)	Total Interest ($)
100,000	4.0	10	1,012.45	121,494.42	21,494.42
250,000	5.0	15	1,976.98	355,856.93	105,856.93
500,000	3.5	20	2,899.65	695,916.01	195,916.01
750,000	4.5	25	4,168.75	1,250,624.57	500,624.57
1,000,000	5.0	30	5,368.22	1,932,558.14	932,558.14
200,000	3.0	10	1,931.17	231,740.05	31,740.05
300,000	6.0	20	2,149.29	515,829.84	215,829.84
150,000	4.0	5	2,762.74	165,764.40	15,764.40
400,000	3.75	15	2,910.26	523,846.86	123,846.86
600,000	5.5	25	3,681.55	1,104,464.49	504,464.49

Frequently Asked Questions

Higher payout frequencies (e.g., monthly vs. annual) mean the principal balance decreases faster because withdrawals occur more frequently. This reduces the average balance earning interest across the life of the annuity. For a $500,000 annuity at 5% over 20 years, switching from annual to monthly payouts typically reduces total interest earned by 2 - 4% of the principal. The tradeoff is receiving income sooner and more regularly.

An ordinary annuity pays at the end of each period; an annuity-due pays at the beginning. Because annuity-due payments occur one period earlier, each payment is discounted by one fewer period. The mathematical result is that the per-period payout for an annuity-due is lower by a factor of 1 ÷ (1 + r) compared to the ordinary annuity. For a 5% annual rate, each annuity-due payment is approximately 4.76% smaller than the corresponding ordinary annuity payment, but you receive the first payment immediately.

The growth rate g models annual payment escalation to offset inflation. A typical value is 2 - 3%. When g = r, the standard growing annuity formula produces a 0 ÷ 0 indeterminate form. In that edge case, the payout simplifies to PMT = PV ÷ n, meaning all payments are equal and the interest earned exactly offsets the growth escalation.

The calculator computes payouts starting from the specified start date based on full periods. It does not prorate the first period. If you begin an annuity mid-year with annual payments, the first payout occurs one full year from the start date. For monthly payouts, the first payment is one full month from the start date. The amortization schedule labels each period with its sequential number relative to the start date.

This calculator models the payout (distribution) phase, not the accumulation phase. To model a deferred annuity, first compute the future value of your investment at the end of the deferral period using compound interest: FV = PV × (1 + r)^n_defer. Then enter that FV as the lump sum in this calculator to determine the periodic payout.

Use the guaranteed crediting rate stated in your annuity contract, not the projected or illustrated rate. Fixed annuities in the US typically offer 3.0 - 5.5% as of 2024. Variable annuity rates fluctuate with underlying investments. This calculator assumes a constant nominal rate compounded at the payout frequency. It does not model variable returns, market-value adjustments, or rider fees that may apply to your specific contract.