Annuity Present Value Calculator
Calculate the present value (today's worth) of a stream of regular future payouts, with total payouts and the discount gap.
Input Data
Results
At a glance:Annuity Present Value calculates what a stream of fixed future payouts is worth in total in today's money. It rests on the time value of money — future money discounted to today is worth less, so discounting each payout at the discount rate and adding them gives a present value that is necessarily lower than the nominal total payouts; the gap is the time-value (discounting) effect. This tool uses the ordinary-annuity (end-of-period) model and is the core tool for valuing the 'today's worth' of a retirement annuity, insurance payout, rental income or instalment receivables. It is the mirror of the Annuity Payout Calculator: one infers today's principal from the periodic payout, the other infers the periodic payout from today's principal. The higher the discount rate and the longer the term, the lower the present value relative to the total payouts.
Formula
Periodic discount rate i = annual discount rate ÷ payouts per year; total periods n = years × payouts per year.
Present value PV = periodic payout × [(1 − (1 + i)^−n) ÷ i].
Total payouts = periodic payout × n; discount gap = total payouts − present value.
$$PV = PMT \times \dfrac{1 - (1 + i)^{-n}}{i}$$How to Use
- Enter the fixed monthly payout you plan to receive in future.
- Enter the annual discount rate (your opportunity cost or market rate) and payout term.
- View the present value (today's worth), nominal total payouts and the discount gap.
FAQ
Why is the total future payout larger than the present value?
Because of the time value of money — a dollar today is worth more than a dollar in the future. Discounting each future payout at the discount rate and adding them up gives a present value that is lower than the nominal total payout; the gap is the time value created by discounting.
What discount rate should I use?
The discount rate usually reflects your opportunity cost — the return you could earn if this money were invested instead, or the market risk-free rate. A higher discount rate means you value current cash more, so the present value is lower. Try different rates to test sensitivity.
How is this related to the Annuity Payout Calculator?
They are two sides of the same coin. The Annuity Present Value works backwards from the periodic payout to today's principal; the Annuity Payout works backwards from today's principal to the periodic payout. If you put the present value from this tool into the payout calculator as the principal, you get back the original periodic payout.
How much does the discount rate affect the present value?
A great deal. Take a monthly payout of HK$5,000 over 15 years: at a 3% discount rate the present value is about HK$724,027, but at 7% it drops to about HK$556,280 — a difference of nearly HK$170,000. The higher the discount rate, the more you value current cash (higher opportunity cost) and the less a stream of future income is worth today. When evaluating an annuity product or a lump-sum cash-out, always run a sensitivity analysis at several discount rates.
Does the present value keep growing without limit as the term lengthens?
No. Although a longer payout term means a larger nominal total, each far-future payout discounts to close to zero, so the increase in present value gradually slows and converges. For a monthly payout of HK$1,000 at a 5% discount rate: 5 years ≈ HK$52,991, 10 years ≈ HK$94,281, 15 years ≈ HK$126,455, 20 years ≈ HK$151,525 — the growth clearly tapers off. If the payout term extends indefinitely, the present value approaches a ceiling; that is the concept of a perpetuity.
Related Tools
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.