Future value: what regular contributions grow into
The accumulation phase of an annuity is the period during which fixed contributions are made into an account and grow at a rate of return until a target future date, such as retirement. This calculator models an ordinary annuity — each payment occurs at the end of each period, the standard convention for most retirement contribution schedules such as 401(k) or IRA payroll deductions.
Worked example: $500 contributed monthly at a 7% annual return for 20 years (240 months) grows to a future value of $260,463.33. Total contributions over that period are $120,000 (240 payments of $500), meaning growth from the rate of return alone accounts for $140,463.33 of the final balance.
- Future value FV = PMT × [((1 + r)^n − 1) ÷ r], where PMT = monthly payment, r = annual rate ÷ 12, n = years × 12
- Total contributions = PMT × n; Growth = FV − total contributions
Present value: what a future payment stream is worth today
Present value answers a different question: given a stream of equal future payments — a pension benefit, a structured settlement, rental income — what is that stream worth today, given a discount rate reflecting the time value of money? Discounting reflects that money available now can earn a return, so a payment arriving in 20 years is worth much less today than one arriving next month.
Worked example: $1,000 a 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 same formula underlies loan mathematics in reverse: a lender advancing $151,525 at 5% for 20 years would charge almost exactly $1,000 a month.
| Discount rate | Present value of $1,000/mo for 20 years |
|---|---|
| 3% | $180,311 |
| 5% | $151,525 |
| 7% | $128,983 |
Payout: what level income a lump sum can sustain
A payout calculation determines the level periodic payment a fixed starting principal can support over a set number of years, structured so the balance is fully exhausted by the end of the period — the reverse of an accumulation calculation. This is sometimes called a period-certain payout, distinct from a lifetime annuity product, which continues paying for as long as the annuitant lives.
Worked example: a $500,000 principal at a 5% annual rate over 25 years (300 months) supports a level monthly payout of $2,922.95 — an annual payout of $35,075.40 — with $876,885.06 paid out in total over the full period. The excess over the original $500,000 principal represents ongoing investment growth during the payout period, which is what allows the payout to exceed simple principal-divided-by-months.
- Monthly payout PMT = P × r ÷ [1 − (1 + r)^−n], where P = principal, r = annual rate ÷ 12, n = years × 12
How the three fit together
Future value, present value and payout are three views of the same underlying annuity mathematics, applied in different directions: future value projects contributions forward into a lump sum; present value discounts a future payment stream back into today's dollars; and payout converts an existing lump sum into a sustainable income stream. All three assume an ordinary annuity (end-of-period payments) and a constant rate for the full period — none of them model taxes, fees, inflation adjustments, or the insurer-specific mortality pricing of a commercially purchased lifetime annuity product.
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How much will $500 a month grow to at 7% over 20 years?
Using the future value of an ordinary annuity formula, $500 monthly at a 7% annual return for 20 years (240 months) grows to $260,463.33 — $120,000 from contributions and $140,463.33 from growth.
What is the present value of a $1,000 monthly payment stream?
It depends on the discount rate and duration. $1,000 a month for 20 years at a 5% discount rate is worth $151,525.31 today, versus $240,000 undiscounted — an $88,474.69 time-value discount.
How much monthly income can $500,000 provide?
At an assumed 5% annual rate of return over 25 years, a $500,000 principal supports a level monthly payout of $2,922.95, fully exhausting the principal by the end of the period.
What's the difference between an ordinary annuity and an annuity due?
An ordinary annuity assumes payments occur at the end of each period; an annuity due assumes payments at the start. Because annuity-due payments compound for one extra period each, they produce a slightly higher future value — and a slightly higher present value, by a factor of about 0.42% at a 5% annual rate — than an otherwise identical ordinary annuity.
Does this model a lifetime annuity from an insurance company?
No. These are period-certain calculations based on a fixed rate of return, principal, and time period. A commercially purchased lifetime annuity includes insurer-specific fees, guarantees, surrender charges and mortality-based pricing that these formulas do not model.
Kaynaklar
- U.S. Securities and Exchange Commission (SEC), Investor.gov — annuities overview and investor bulletins. https://www.investor.gov/
- Financial Industry Regulatory Authority (FINRA) — Annuities: how they work and what to consider. https://www.finra.org/
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. 13th ed. McGraw-Hill Education, 2020 — annuity mathematics.