Understanding your present value result
The discount rate drives the valuation heavily. The table reprices the worked example's $1,000/month, 20-year stream at different rates — higher rates make future money worth less today.
| Discount rate | Present value of $1,000/mo for 20 years |
|---|---|
| 3% | $180,311 |
| 5% | $151,525 |
| 7% | $128,983 |
- This models an ordinary annuity (end-of-month payments); an annuity due (start-of-month) is worth a factor of (1+r) more — about 0.42% at 5%.
- The payments are assumed fixed; valuing an inflation-indexed stream requires a real (inflation-adjusted) discount rate instead of a nominal one.
- The result is highly sensitive to the discount rate, which is a judgment about alternative returns and risk — pension and settlement offers often embed a rate less favorable than the recipient's alternatives.
- Educational calculation only; evaluating an actual buyout, settlement, or annuity purchase involves taxes, credit risk, and longevity considerations beyond this formula.
What is the present value of an annuity?
An annuity, in the time-value-of-money sense, is any stream of equal payments at regular intervals — a pension benefit, loan payments, lease payments, a structured legal settlement, or bond coupons. Its present value is the single amount today that is financially equivalent to the whole stream, computed by discounting each payment back at a chosen rate. The concept is core curriculum in corporate finance and in the CFA Institute's quantitative methods material.
Discounting reflects that money available now can earn a return: a payment arriving in 20 years is worth much less today than one arriving next month. Summing the discounted payments gives a figure well below the simple total — in the worked example, 240 monthly payments of $1,000 total $240,000 nominally, but at a 5% discount rate they are worth $151,525 today. The $88,475 gap is the time-value discount.
This calculation is the mathematical basis for pricing loans (a loan principal is the present value of its payments), valuing pension buyout offers, comparing lottery lump-sum versus annuity options, and pricing fixed-income instruments. This calculator models an ordinary annuity — payments at the end of each month; a stream paying at the beginning of each period (annuity due) is worth one month's interest more.
How to use this present value of annuity calculator
- Enter the payment received (or paid) each month.
- Enter the annual discount rate — the return the money could earn in a comparable alternative, or the rate offered in the deal you are evaluating.
- Enter how many years the payments continue.
- Read the present value, the undiscounted sum of the payments, and the discount between the two.
- Worked example: $1,000 per month for 20 years at a 5% discount rate has a present value of $151,525.31, versus $240,000 of undiscounted payments — a time-value discount of $88,474.69.
The present value of annuity formula
Each payment is discounted by (1+r) raised to the number of months until it arrives; summing the geometric series gives the closed-form annuity factor [1 − (1+r)^−n] ÷ r. Multiplying the payment by this factor gives the present value of an ordinary annuity (end-of-period payments).
The same formula underlies loan mathematics in reverse: a lender advancing $151,525 at 5% for 20 years would charge almost exactly $1,000 per month. The time-value discount is the undiscounted total minus the present value — the aggregate interest embedded in the stream.
Common mistakes
- Comparing a lump-sum offer against the undiscounted total of payments — $240,000 of future payments is not worth $240,000 today; the fair comparison is against the present value.
- Using an annual formula on monthly payments (or vice versa) — the rate and period count must match the payment frequency.
- Ignoring whether payments arrive at the start or end of each period; annuities due are worth (1+r) times more than ordinary annuities.
- Applying a nominal discount rate to inflation-indexed payments, which undervalues the stream.
- Treating the discount rate as objective — small changes move the valuation a lot, and whoever sets the rate in an offer shapes the outcome.
Häufig gestellte Fragen
What is the present value of $1,000 a month for 20 years?
At a 5% annual discount rate, $151,525.31 — the formula PV = 1000 × [1 − (1 + 0.05/12)^−240] ÷ (0.05/12). The 240 payments total $240,000 nominally; the $88,475 difference is the time-value discount, reflecting that most of those payments arrive years in the future. At a 3% rate the stream is worth $180,311; at 7%, $128,983.
What discount rate should I use to value an annuity?
The return available on a comparable alternative with similar risk and duration. For evaluating a safe payment stream, yields on Treasury securities of matching maturity are a common benchmark; for riskier streams, a higher rate applies. The choice matters greatly — the worked example's valuation moves by roughly $29,000 between 3% and 5% — which is why offers should be tested at several rates.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period (most loans and bonds); an annuity due pays at the beginning (most rents and many insurance payouts). Each payment in an annuity due arrives one period sooner, so its present value is higher by a factor of (1+r) — about 0.42% for monthly payments at a 5% annual rate. This calculator models the ordinary form.
How is this used to evaluate a pension buyout or settlement offer?
Compute the present value of the payment stream being given up, at a discount rate reflecting your realistic alternatives, and compare it to the lump sum offered. If the lump sum is materially below the present value, the offer embeds an unfavorable rate. Real decisions also involve taxes, the payer's credit risk, inflation protection, and longevity, so the present value is the starting point, not the whole analysis — and not financial advice.
Why is the present value so much less than the total of the payments?
Because money has time value: a payment arriving in year 19 could have been earning the discount rate for 19 years if received today, so its present equivalent is much smaller. At 5%, a $1,000 payment due in 20 years is worth only about $369 today. Summing 240 such discounted values gives $151,525 rather than $240,000 — the later the payment, the deeper its discount.
Quellenangaben
- CFA Institute. Quantitative Methods — the time value of money. CFA Program Curriculum.
- Ross SA, Westerfield RW, Jordan BD. Fundamentals of Corporate Finance. 13th ed. McGraw-Hill Education, 2021 — discounted cash flow valuation.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. 13th ed. McGraw-Hill Education, 2020.
- U.S. Securities and Exchange Commission (SEC). Investor.gov — annuities investor information. investor.gov.