Finance

Annuity Calculator

Calculate the present value and future value of an annuity. Choose between ordinary annuity and annuity due, and view a full payment schedule.

Quick Answer

An annuity's present value uses PV = PMT × [(1 - (1+r)-n) / r] and future value uses FV = PMT × [((1+r)n - 1) / r]. For example, $1,000/year at 6% for 20 years has a PV of $11,470 and FV of $36,786. Annuity due values are (1 + r) times higher.

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150

Annuity Values (Ordinary)

Present Value

$11,470

What all payments are worth today

Future Value

$36,786

Accumulated value at end

Total Payments
$20,000
Total Interest (FV)
$16,786
Interest/Payment Ratio
83.9%

Accumulation Over Time

BalancePayments
Period 1Period 10Period 20

Payment Schedule

PeriodPaymentInterestBalance
1$1,000.00$0.00$1,000.00
2$1,000.00$60.00$2,060.00
3$1,000.00$123.60$3,183.60
4$1,000.00$191.02$4,374.62
5$1,000.00$262.48$5,637.09
6$1,000.00$338.23$6,975.32
7$1,000.00$418.52$8,393.84
8$1,000.00$503.63$9,897.47
9$1,000.00$593.85$11,491.32
10$1,000.00$689.48$13,180.79
11$1,000.00$790.85$14,971.64
12$1,000.00$898.30$16,869.94
13$1,000.00$1,012.20$18,882.14
14$1,000.00$1,132.93$21,015.07
15$1,000.00$1,260.90$23,275.97
16$1,000.00$1,396.56$25,672.53
17$1,000.00$1,540.35$28,212.88
18$1,000.00$1,692.77$30,905.65
19$1,000.00$1,854.34$33,759.99
20$1,000.00$2,025.60$36,785.59
Disclaimer: This calculator provides estimates for educational purposes only. Actual annuity products from insurance companies may have different terms, fees, and guarantees. Consult a qualified financial advisor before purchasing any annuity product or making investment decisions.

About This Tool

The Annuity Calculator computes both the present value and future value of an annuity — a series of equal payments made at regular intervals. Whether you are evaluating retirement income streams, comparing lease payments, pricing bonds, or planning a savings program, understanding annuity math is essential for sound financial decision-making.

The Annuity Formulas

For an ordinary annuity (payments at end of period):

  • PV = PMT × [(1 - (1 + r)-n) / r]
  • FV = PMT × [((1 + r)n - 1) / r]

For an annuity due (payments at beginning of period), multiply each formula by (1 + r).

Where PMT is the payment per period, r is the interest rate per period, and n is the total number of periods.

Ordinary Annuity vs. Annuity Due

The timing of payments matters more than you might expect. An annuity due pays at the start of each period, so each payment has one extra period to earn interest. The difference equals exactly (1 + r) times the ordinary annuity value. For a 6% rate, that is a 6% premium — significant over many periods. Rent and insurance premiums are common annuities due; mortgage and bond coupon payments are ordinary annuities.

Present Value: What It Means

The present value tells you the lump sum equivalent of the annuity stream today. If someone offered you $1,000/year for 20 years at 6%, you would need $11,470 invested today to replicate that income stream. This concept is critical for pricing pensions, structured settlements, lottery winnings (lump sum vs. annuity), and any situation where you are choosing between a stream of payments and a lump sum.

Future Value: Accumulation Power

The future value shows what your periodic investments will grow to over time. Saving $1,000/year at 6% for 20 years accumulates to $36,786 — nearly double your $20,000 in total payments. The difference ($16,786) is pure compound interest. This demonstrates why consistent periodic investing, combined with compound growth, is the most reliable path to wealth accumulation.

Real-World Applications

  • Retirement planning: Calculate how much periodic contributions will grow to (FV) or how much you need saved to fund retirement withdrawals (PV).
  • Loan analysis: The PV formula underlies mortgage, car loan, and student loan payment calculations.
  • Lease valuation: Compare the PV of lease payments to the purchase price to determine the better deal.
  • Bond pricing: A bond's price is the PV of its coupon payments (an annuity) plus the PV of its face value at maturity.

The Payment Schedule

The payment schedule table shows period-by-period accumulation. Notice how interest earned grows each period as the balance increases — this is the compounding effect in action. In the early periods, most of the balance growth comes from payments. In later periods, interest increasingly dominates. This hockey-stick pattern is why time in the market matters more than timing the market.

Frequently Asked Questions

What is an annuity?
An annuity is a series of equal payments made at regular intervals over a specified period. In finance, annuities appear in many contexts: mortgage payments, retirement income streams, insurance payouts, bond coupon payments, and lease obligations. The two main types are ordinary annuities (payments at the end of each period) and annuities due (payments at the beginning).
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity, payments occur at the end of each period (e.g., mortgage payments). In an annuity due, payments occur at the beginning of each period (e.g., rent payments, insurance premiums). Because annuity due payments happen one period earlier, they have slightly higher present and future values — exactly (1 + r) times the ordinary annuity values, where r is the interest rate per period.
What is the present value of an annuity?
The present value (PV) of an annuity is today's equivalent value of all future annuity payments, discounted at the appropriate interest rate. It answers: 'How much would I need to invest today to fund all future payments?' For an ordinary annuity: PV = PMT x [(1 - (1+r)^-n) / r]. The PV is always less than the sum of all payments because money received in the future is worth less than money today.
What is the future value of an annuity?
The future value (FV) of an annuity is the total accumulated value of all payments plus compound interest at the end of the annuity's term. It answers: 'How much will all my periodic investments be worth in the future?' For an ordinary annuity: FV = PMT x [((1+r)^n - 1) / r]. The FV is always more than the sum of payments because each payment earns interest for a different number of periods.
How do I use the annuity calculator for retirement planning?
For accumulation phase: enter your periodic contribution as the payment, expected annual return as the rate, and years until retirement as periods. The FV shows your projected retirement nest egg. For distribution phase: enter your desired annual withdrawal, a conservative growth rate, and years in retirement. The PV tells you how much you need saved at retirement to fund those withdrawals.
What happens if the interest rate is 0%?
At 0% interest, both PV and FV of an annuity equal the simple sum of all payments (PMT x n). There is no time value of money effect — a dollar today is worth exactly the same as a dollar in the future. While unrealistic for most scenarios, this serves as a useful baseline. In real terms (after inflation), 0% represents maintaining purchasing power exactly.

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