Annuity Calculator

An annuity is a pattern: equal payments made at regular intervals. In personal finance, that pattern can describe monthly deposits into an investment account, systematic withdrawals from a retirement balance, rent-like payments, or the mathematical core of an insurance annuity. This calculator focuses on the math concept rather than the insurance product. It grows an opening balance, values the stream of equal payments, and reports either a future value or a remaining balance after withdrawals.

That broad setup makes this the overview page for the annuity family. If you only need the value today of promised future payments, use the present value of annuity calculator. If you are building savings from equal contributions with no separate opening-balance decision, compare the future value of annuity calculator. If you already know the lump sum and want the regular income it can support, the annuity payout calculator is more focused. For payments with no fixed end date, use the perpetuity calculator.

What the calculator does

The form has two modes. Deposit / grow adds the payment stream to the opening balance and returns a future value. Withdrawal / payout subtracts the payment stream from the opening balance and returns the balance left after the selected period. In both modes, the annual rate is converted to a periodic rate by dividing by the payment frequency. The number of periods is the length in years times that frequency, rounded to the nearest whole payment count.

The result panel also shows total deposits or withdrawals, investment return, number of payments, and the periodic rate. In withdrawal mode, it includes an estimated sustainable payment. That sustainable figure is the regular withdrawal that would use the grown opening balance over the selected schedule, assuming the same rate and timing.

Formula

Let the opening balance be PV, the regular payment be PMT, the periodic return be i, and the rounded number of payments be n. The calculator first computes the growth factor and the payment-stream factor:

$\text{growth factor} = (1+i)^n$

$\text{payment factor} = \frac{(1+i)^n - 1}{i}$

When the periodic rate is zero, the payment factor is n. For a deposit annuity with end-of-period payments, the result is:

$\text{future value} = \text{PV} \times (1+i)^n + \text{PMT} \times \frac{(1+i)^n - 1}{i}$

For a withdrawal annuity, the payment-stream part is subtracted:

$\text{ending balance} = \text{PV} \times (1+i)^n - \text{PMT} \times \frac{(1+i)^n - 1}{i}$

For annuity-due timing, the payment-stream part is multiplied by one extra period of growth:

$\text{timing factor} = 1+i$

That timing factor is applied to deposits and withdrawals because beginning-of-period cash flows happen one period earlier than ordinary annuity cash flows.

Example

The default deposit example starts with an opening balance of $10,000, adds $500 monthly, uses a 6% annual rate, runs for 10 years, and assumes ordinary end-of-month payments. The calculator rounds 10 years times 12 payments per year to 120 payments. The periodic rate is 6% divided by 12, or 0.5% per month.

With those inputs, the growth factor is about 1.819396734. The $10,000 opening balance grows to $18,193.97. The ordinary payment factor is about 163.879346806, so the $500 monthly stream contributes $81,939.67. Add the two parts and the future value is $100,133.64. Total deposits are $60,000, so the calculator reports investment return of $30,133.64 after subtracting the opening balance and deposits from the ending value.

Switching the same example to annuity due multiplies only the payment stream by 1.005. That does not change the opening balance growth, but it gives every monthly deposit one extra month of return. The result is higher for deposits. In withdrawal mode, the same timing choice lowers the sustainable payment because money leaves the account earlier.

Ordinary annuity versus annuity due

The timing choice is small in one period and meaningful over many periods. An ordinary annuity works like a payment made after the period has elapsed: a monthly contribution at month-end, a bond coupon paid at the end of a coupon period, or a scheduled withdrawal after that month’s investment return has been credited. An annuity due works like rent paid at the start of the month: the payment occurs before the period’s growth.

For deposits, annuity due produces a larger future value than ordinary timing when the rate is positive. For withdrawals, beginning-of-period payouts draw down the balance earlier, so the same withdrawal amount leaves a lower ending balance. The difference grows when the rate is higher, the payment is larger, or the schedule has many periods.

Insurance product versus math concept

The word annuity can mean either a cash-flow pattern or a contract sold by an insurance company. This calculator handles the cash-flow pattern. It does not price mortality credits, life-contingent income, surrender charges, guaranteed minimum benefits, inflation riders, market value adjustments, premium taxes, or insurer-specific rules. Those features can make a real annuity contract pay more or less than a simple account drawdown.

Use this page for transparent time-value-of-money comparisons. For example, it can show how a $1,500 monthly withdrawal compares with a $250,000 portfolio at a 4% assumed return. In that scenario, 15 years of monthly ordinary withdrawals leaves about $85,939.67, and the sustainable payment is about $1,849.22 per month. That result is not a promise; it is a way to see whether the payment size is internally consistent with the rate and term you entered.

Tips for better inputs

• Match the payment frequency to the real cash flow. Monthly contributions should use monthly frequency, not annual frequency.
• Use a net return when possible. If investment fees or insurance charges are known, subtract them from the expected return before entering the rate.
• Keep the rate and payment schedule consistent. A nominal annual return divided by the payment frequency is a simple planning assumption, not a full investment forecast.
• Test stress cases. Lower the return, shorten the accumulation period, or raise the withdrawal amount to see how sensitive the ending balance is.
• Treat negative balances as a warning that the planned withdrawal stream is too large for the selected assumptions.

Informational note

This calculator is for education and planning. It does not provide investment, tax, legal, or insurance advice. Before buying an annuity product or committing to a retirement withdrawal plan, compare contract terms, liquidity, fees, guarantees, beneficiary rules, and tax treatment with a qualified professional.

Sources

• SEC Investor.gov, Annuities — overview of annuity contracts, types, income streams, and investor considerations.
• FINRA, Annuities — overview of annuity types, benefits, risks, and sales considerations.