The Annuity Formula Explained

Annuity math is built on the time value of money — the principle that a dollar today is worth more than a dollar in the future. There are two primary scenarios: calculating how much a sum grows (future value), and calculating how much regular income a sum can generate (present value / payout).

Future Value of a Lump Sum

If you deposit a single amount and let it compound:

FV = PV × (1 + r)^n

Where PV = present value, r = interest rate per period, n = number of periods. Example: $100,000 at 5% annually for 20 years → FV = $100,000 × (1.05)^20 = $265,330.

Future Value with Regular Contributions

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

Where PMT = periodic payment, type = 0 for ordinary annuity (end of period), type = 1 for annuity due (beginning). If you contribute $500/month for 20 years at 5% annually (r = 0.4167%/month, n = 240): FV ≈ $205,516.

Monthly Payout from a Lump Sum

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

This tells you how much monthly income a balance can generate. A $200,000 annuity at 5% annual over 20 years (r = 0.4167%, n = 240) generates a monthly payment of approximately $1,320.

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Total Contributed
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Ordinary Annuity vs. Annuity Due

An ordinary annuity makes payments at the end of each period. Most mortgages, retirement accounts, and investment products work this way. An annuity due makes payments at the start — rent and insurance premiums are classic examples. The annuity due is worth slightly more because each payment gets one additional compounding period. On a $1,000/month contribution over 30 years at 6%, an annuity due yields about $47,000 more in future value than an ordinary annuity.

Common Mistakes When Calculating Annuities

The most frequent error is mismatching the rate period with the payment period. If payments are monthly, the rate must be the monthly rate (annual ÷ 12) and n must be in months (years × 12). Using annual rates with monthly periods overstates growth significantly. The second mistake is forgetting that the payout rate and accumulation rate are different numbers when buying an insurance annuity product — see our annuity payout calculator for the distribution-phase formula.

Frequently Asked Questions

What is the formula to calculate annuity future value?
The future value formula for a lump sum is FV = PV × (1 + r)^n. For periodic payments, use FV = PMT × [((1 + r)^n − 1) / r]. Here, r is the interest rate per period, n is the total number of periods, PV is the present value, and PMT is the payment per period. For an annuity due, multiply the result by (1 + r). These are the same formulas used in financial planning software and actuarial exams.
What is the difference between an ordinary annuity and annuity due?
An ordinary annuity makes payments at the end of each period — most mortgages, car loans, and retirement withdrawals work this way. An annuity due makes payments at the beginning of each period — rent, insurance premiums, and lease payments are common examples. Annuity due is slightly more valuable because each payment compounds for one extra period, resulting in a higher future value. Our main annuity calculator lets you toggle between both types.
How do I calculate monthly annuity payments?
Use PMT = PV × [r(1+r)^n] / [(1+r)^n − 1], where r is the monthly interest rate (annual ÷ 12) and n is total months. For example, $200,000 at 5% annually over 20 years gives r = 0.4167% and n = 240, resulting in monthly payments of approximately $1,320. You can also use our payout calculator which handles this formula automatically.
Can I calculate an annuity in Excel?
Yes. Excel includes built-in functions: FV(rate, nper, pmt, pv) for future value, PV(rate, nper, pmt) for present value, and PMT(rate, nper, pv) for periodic payments. For example, =PMT(5%/12, 240, -200000) returns the monthly payment from a $200,000 annuity over 20 years at 5%. Our online calculator uses identical formulas and is faster for quick comparisons without opening a spreadsheet.

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