An annuity is a series of equal periodic payments made over a set number of periods. In finance, an annuity can refer to either an investment product that pays out income or the mathematical concept of a fixed stream of cash flows. Ordinary annuities (most common) have payments at the end of each period. Annuities-due have payments at the beginning. Examples include mortgage payments, lease payments, and retirement pension income.

Annuity Calculator

Q: How do I calculate the present value of an annuity?

The present value (PV) of an ordinary annuity is PV = PMT × [1 − (1+r)^−n] / r, where PMT is the periodic payment, r is the periodic interest rate, and n is the number of periods. For example, a $1,000/month annuity for 10 years at 5%/year (0.4167%/month) has a PV of $1,000 × [1 − (1.004167)^−120] / 0.004167 = $94,281. This is the lump sum needed today to fund those payments.

Q: Is annuity income taxable?

Yes, but only the interest/growth portion is taxable, not the return of principal. For a non-qualified annuity (purchased with after-tax dollars), withdrawals are taxed on a last-in-first-out (LIFO) basis - the growth is withdrawn first and taxed as ordinary income. For a qualified annuity (held in an IRA or 401k), the entire withdrawal is taxable. The exclusion ratio applies to immediate annuities purchased with non-qualified funds, prorating the taxable and non-taxable portions.

Calculate annuity future value, payment, or present value instantly.

📊 What is an Annuity?

An annuity is a series of equal periodic payments made over a fixed number of periods at a constant interest rate. The word "annuity" comes from the Latin annuus (annual), but annuities can have monthly, quarterly, or annual payment intervals. Annuities appear throughout personal finance: mortgage payments, car loans, lease payments, pension income, and structured settlement payments are all annuities in the mathematical sense.

There are two fundamental types based on when payments occur. In an ordinary annuity (also called annuity-immediate), payments occur at the end of each period. Most loans and bonds are ordinary annuities. In an annuity-due, payments occur at the beginning of each period - rent, insurance premiums, and lease payments typically follow this pattern. An annuity-due has a slightly higher value than an equivalent ordinary annuity because each payment earns one extra compounding period.

In the insurance and retirement context, an annuity is a contract with an insurance company. You pay a lump sum (or series of premiums), and the insurer promises a guaranteed income stream for a fixed period or for life. This calculator focuses on the mathematical calculation of ordinary and annuity-due cash flows and can solve for future value, present value, or the periodic payment given the other variables.

📐 Annuity Formula

FV (ordinary) = PMT × [(1+r)ⁿ − 1] / r

FV (annuity-due) = PMT × [(1+r)ⁿ − 1] / r × (1+r)

PV (ordinary) = PMT × [1 − (1+r)−ⁿ] / r

PMT = FV × r / [(1+r)ⁿ − 1]

PMT = Periodic payment amount

r = Interest rate per period (annual rate / periods per year)

n = Total number of periods

FV = Future value (accumulated amount)

PV = Present value (lump sum equivalent today)

All annuity calculations derive from the time-value-of-money principle: a dollar today is worth more than a dollar in the future. The annuity formula aggregates the compounded future value (or discounted present value) of each individual payment. Annuity-due is always greater than ordinary annuity by exactly (1+r), reflecting the one extra period of compounding for each payment.

📖 How to Use This Calculator

Steps

Select what to solve for - Future Value (total accumulated), Present Value (lump sum equivalent), or Payment (required periodic payment).

Enter the known values - payment amount (or target FV), annual interest rate, and number of years.

Choose annuity type - ordinary (end of period, most loans/investments) or annuity-due (beginning of period, most leases/rent).

Click Calculate to see the result along with total payments and interest earned or saved.

💡 Example Calculations

Example 1 - Future Value of Monthly Savings

PMT = $500/month | Rate = 6%/year | 20 years | Ordinary Annuity

Monthly rate r = 6% / 12 = 0.5% = 0.005; n = 20 × 12 = 240 months

FV = $500 × [(1.005)²⁴⁰ − 1] / 0.005 = $500 × 462.04 = $231,020

Total Paid = $500 × 240 = $120,000 | Interest Earned = $111,020

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Example 2 - Present Value of Pension Income

PMT = $2,000/month | Rate = 5%/year | 20 years | Ordinary Annuity

Monthly rate = 5/12/100 = 0.4167%; n = 240

PV = $2,000 × [1 − (1.004167)−²⁴⁰] / 0.004167 = $302,068

Lump sum needed today = $302,068 to fund $2,000/month for 20 years at 5%

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❓ Frequently Asked Questions

What is an annuity?+

An annuity is a series of equal periodic payments made over a fixed number of periods at a constant interest rate. Examples include mortgage payments, car loans, lease payments, pension income, and structured settlement payments. In the insurance/retirement context, an annuity is a contract where you pay a lump sum and receive guaranteed income payments.

What is the difference between an ordinary annuity and annuity-due?+

In an ordinary annuity, payments occur at the end of each period (e.g., a monthly mortgage payment due at month-end). In an annuity-due, payments occur at the beginning of each period (e.g., rent paid on the 1st of the month). Because annuity-due payments are received one period earlier, the future value of an annuity-due is higher by a factor of (1+r) compared to an ordinary annuity with identical terms.

How do I calculate the present value of an annuity?+

The present value (PV) of an ordinary annuity is: PV = PMT × [1 − (1+r)^−n] / r, where PMT is the periodic payment, r is the periodic interest rate, and n is the number of periods. For example, a $1,000/month annuity for 10 years at 5%/year has a PV of approximately $94,281 - that is the lump sum needed today to fund those payments.

What is a good annuity return rate?+

Fixed annuity rates in the US (as of 2024) range from about 4% to 6% depending on term length and insurer. Multi-year guaranteed annuities (MYGAs) for 3–5 years often pay 4.5–5.5%. Variable annuities depend on the underlying investments. Income annuities are priced based on prevailing interest rates and mortality tables rather than a stated return rate.

Is annuity income taxable?+

Yes, but only the interest/growth portion is taxable for non-qualified annuities (purchased with after-tax dollars). Withdrawals are taxed on a last-in-first-out (LIFO) basis - the growth is withdrawn first and taxed as ordinary income. For qualified annuities (held in an IRA or 401k), the entire withdrawal is taxable. The exclusion ratio applies to immediate annuities, prorating the taxable and non-taxable portions of each payment.

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📌 Quick Tips

💡An annuity-due (payments at the start of each period) is worth slightly more than an ordinary annuity because each payment earns one extra period of interest.

💡Fixed annuities guarantee a set payment; variable annuities tie payments to investment performance. This calculator models fixed/guaranteed-rate annuities.

💡The present value of an annuity tells you the lump sum you'd need today to generate a given stream of future payments at a given rate.