Quick answer
A lottery annuity pays growing yearly instalments, with the first payment x solving Σ x(1 + g)ᵏ = prize. A $100,000,000 prize paid over 30 years with 5% yearly increases starts at $1,505,143.51, ends at $6,195,374.77 and has an estimated cash value of $52,053,422.03 at a 4% discount rate.
Enter the prize, number of yearly payments, yearly increase and discount rate. The calculator returns the first and last payments and the cash value.
Related tools: Annuity Calculator: Future and present value of a series of equal payments. Annuity Payout Calculator: Monthly payout that exhausts a balance over a set number of years.
How to use the Lottery Annuity Calculator
- Enter total annuity prize ($) (above 0).
- Enter number of yearly payments (a whole number, between 2 and 100).
- Enter yearly increase in payments (%) (between 0 and 50).
- Enter discount rate (%) (between 0 and 100).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Total annuity prize | A number, in $ | > 0 |
| Number of yearly payments | A whole number | ≥ 2, ≤ 100 |
| Yearly increase in payments | A number, in % | ≥ 0, ≤ 50 |
| Discount rate | A number, in % | ≥ 0, ≤ 100 |
Formula and method
Formula
first payment x solves Σ x(1 + g)ᵏ = total; value = Σ x(1 + g)ᵏ ÷ (1 + d)ᵏ, k = 0 … n − 1
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Payments are received at the start of each year (the first one immediately); taxes are not modeled and the discount rate is your own assumption.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Total annuity prize = 100000000; Number of yearly payments = 30; Yearly increase in payments = 5; Discount rate = 4.
| Result | Value |
|---|---|
| Estimated cash value | $52,053,422.03 |
| First payment | $1,505,143.51 |
| Last payment | $6,195,374.77 |
Example 2
Inputs: Total annuity prize = 1000000; Number of yearly payments = 20; Yearly increase in payments = 0; Discount rate = 3.
| Result | Value |
|---|---|
| Estimated cash value | $766,189.96 |
| First payment | $50,000.00 |
| Last payment | $50,000.00 |
The first line is the headline result (estimated cash value). Below it the lottery Annuity Calculator lists first payment and last payment, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Why the cash value is lower
Money received later is worth less today. Discounting each payment at 4% gives a present value of about 52% of the headline prize. Lotteries offer a lump-sum cash option that is often similar to this present value.
Taxes not included
Federal and state taxes are not modelled. A zero growth rate gives equal payments. The discount rate you choose changes the result sharply, so test several. This is not financial advice.
How the result changes with total annuity prize
Holding every other input at the first worked example, this table changes only total annuity prize. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Total annuity prize | Estimated cash value | First payment | Last payment |
|---|---|---|---|
| 50000000 | $26,026,711.01 | $752,571.75 | $3,097,687.38 |
| 100000000 | $52,053,422.03 | $1,505,143.51 | $6,195,374.77 |
| 200000000 | $104,106,844.06 | $3,010,287.02 | $12,390,749.54 |
| 400000000 | $208,213,688.11 | $6,020,574.03 | $24,781,499.08 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Total annuity prize: entering "0" shows "Total annuity prize must be greater than 0." beside that field and no result.
- Number of yearly payments: entering "1" shows "Number of yearly payments must be at least 2." beside that field and no result.
Choosing between the Lottery Annuity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Annuity Calculator](/finance/annuity-calculator/) | payment each period, annual rate and years | Future value |
| [Annuity Payout Calculator](/finance/annuity-payout-calculator/) | starting balance, annual return and payout period | Monthly payout |
| [Lottery Payout Calculator](/finance/mega-millions-payout/) | cash option of the jackpot, number of winning tickets sharing the prize and federal tax rate | After-tax payout per winner |
| [Present Value of Annuity Calculator](/finance/present-value-of-annuity/) | payment per period, rate per period and number of periods | Present value |
| [Future Value of Annuity Calculator](/finance/future-value-of-annuity/) | payment per period, rate per period and number of periods | Future value |
Background: personal finance estimates
Financial calculators project from the numbers you give them. Long-range tools depend on guesses about returns and tax rates that are unlikely to hold exactly, payoff tools assume a fixed payment and rate, and tax or salary results depend on the tax year, filing status and country. Official calculators say their output is for reference only.
For decisions that matter, use conservative inputs and check the figures against your lender, plan documents or a qualified adviser.
Assumptions and limitations
- Zero growth gives equal payments
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for total annuity prize and number of yearly payments to confirm this.
Frequently asked questions
Is annuity or lump sum better?
It depends on taxes, discipline and investment returns.
Why do payments grow?
Many lotteries increase payments by 5% a year.
What discount rate should I use?
A rate close to what you could earn safely.
What does the Lottery Annuity Calculator calculate?
Cash value of an annuity-style prize with yearly increases. It returns Estimated cash value, First payment and Last payment.
What formula does the Lottery Annuity Calculator use?
first payment x solves Σ x(1 + g)ᵏ = total; value = Σ x(1 + g)ᵏ ÷ (1 + d)ᵏ, k = 0 … n − 1. Payments are received at the start of each year (the first one immediately); taxes are not modeled and the discount rate is your own assumption.
What do I need to enter in the lottery Annuity Calculator?
You enter Total annuity prize ($), Number of yearly payments, Yearly increase in payments (%) and Discount rate (%).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Zero growth gives equal payments.
What is an example of a lottery Annuity result?
With total annuity prize 100000000, number of yearly payments 30, yearly increase in payments 5 and discount rate 4, the estimated cash value is $52,053,422.03.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Zero growth gives equal payments.
Related calculators
- Annuity Calculator — Future and present value of a series of equal payments.
- Annuity Payout Calculator — Monthly payout that exhausts a balance over a set number of years.
- Present Value of Annuity Calculator — Present value of equal payments at the end of each period.
- Future Value of Annuity Calculator — Future value of equal payments at the end of each period.
- Lottery Tax Calculator — Take-home from a prize after the tax rates you enter.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.