Skip to content
Calcapedia
Menu
Money

Annuity Calculator

Find what a series of equal payments grows to, what it's worth today, or the steady payout a lump sum can support. Payments can come at the start or end of each period.

Level: Grades 11–12

  • Common Core standard HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Printable worksheet

Annuity Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Calculate
Payments are made at the

Result

Future value

$231,020.45

240 payments of $500.00 at 6% grow to $231,020.45, including $111,020.45 of interest.

Total of payments
$120,000.00
Interest earned
$111,020.45
What the future value is made of
  • Payments$120,000.0051.9%
  • Interest$111,020.4548.1%

See the step-by-step solution ↓

Step-by-step solution

  1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

    i=0.0612=0.005

  2. Count the payments (N): 12 a year for 20 years

    N=12×20=240

  3. Grow each payment with interest to the end of the term, then add them all up

    $500.00×(1+0.005)240−10.005=$231,020.45

  4. Take away what you paid in to see how much interest you earned

    $231,020.45−$120,000.00=$111,020.45

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

How to solve this on a calculator

The keys to press to get this page's worked-example answer on an ordinary calculator, with what the display should show after each step. A named-model tab follows that calculator's official guidebook.

Future value of monthly deposits, with CPT FV

Problem
You save $500 at the end of every month for 20 years in an account earning 6% a year, compounded monthly. What do the deposits grow to?
Formula
FV from N = 240, I/Y = 6, PV = 0, PMT = −500
Example values
N = 240 (months); I/Y = 6 (annual rate, percent); PMT = −500 (monthly deposit (paid in)). These are the fixed values from the worked example on this page, so the keys stay the same whatever you type into the calculator above.
Why a financial calculator
An annuity is a stream of equal payments, which is exactly what the PMT key holds; CPT FV adds up their growth.
The whole sequence
CLR TVM12P/YEND240N6I/Y0PV500±PMTCPTFV

Step by step

  1. CLR TVM

    Press CLR TVM so nothing left over from an earlier problem (such as an old FV) changes the answer.

    Display: TVM cleared

  2. 12P/Y

    Type 12 and press P/Y: monthly deposits. C/Y (compounding per year) is set to the same value.

    Display: P/Y=12

  3. END

    Press END: each payment is made at the end of its period.

    Display: END

  4. 240N

    240 N: 20 years × 12 months.

    Display: N=240

  5. 6I/Y

    6 I/Y: the annual rate.

    Display: I/Y=6

  6. 0PV

    0 PV: the account starts empty.

    Display: PV=0

  7. 500±PMT

    500 ± PMT: each deposit is paid in, so negative.

    Display: PMT=-500

  8. CPTFV

    CPT FV: about $231,020.45, positive because you could take it out.

    Display: FV=231,020.447581

If your answer looks wrong

  • Sign convention: money you receive is positive and money you pay out is negative. The deposits are negative and the balance positive. With PMT = +500 the answer has the opposite sign, -231,020.447581.
  • P/Y and C/Y: with P/Y left at 1, 6 I/Y is applied every month for 240 months and CPT FV shows 9,867,929,787.82. This site's keypad starts with P/Y = C/Y = 1, and setting P/Y also sets C/Y; on a calculator where C/Y doesn't follow P/Y, set C/Y to the same value too, or the monthly rate is worked out from a different compounding.
  • Deposits at the start of each month (an annuity due) need BGN: CPT FV then shows 232,175.549819.

How this is checked: an automated test presses these keys on this site's financial calculator, checks every display along the way, and confirms the answer matches the calculator on this page (last checked 2026-10-19). It has not been checked on any particular brand or model, and real calculators label some keys differently.

What this calculator does

See what a steady series of equal payments is really worth, now or later. In money terms, a series like this is called an annuity. Monthly savings deposits, a pension, lease payments and retirement withdrawals are all examples. Each payment arrives at a different time, so you can't just add them up. You also have to count the interest they earn, or could have earned.

The calculator has three modes. Future value shows what your deposits will grow to by the last payment. Present value shows what a promised series of payments is worth as one lump sum today. Payout works the other way around. It finds the same-size payment a starting balance can fund for a set number of years before it runs out.

Where it's used

Why this math matters outside the classroom:

  • Regular deposits. Depositing $500 a month for 20 years at 6% a year, compounded monthly, grows to about $231,020.
  • Pricing a payout. Paying out $1,000 a month for 20 years at 5% a year needs about $151,525 set aside at the start.
  • Lottery choices. Winners compare a lump sum with an annual payout by finding the present value of the yearly payments.
  • Lease payments. Accountants find the present value of a series of equal lease payments to record them on a balance sheet.
  • Due versus ordinary. Payments made at the start of each period earn one extra period of interest, so an annuity due is worth more than an ordinary annuity.

Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what you want to find: the future value of your payments, their present value, or the payout from a balance.
  2. Enter the payment amount. In payout mode, enter the starting balance instead.
  3. Enter the yearly interest rate, the number of years and how many payments you make each year.
  4. Choose whether payments happen at the end of each period (an ordinary annuity) or at the start (an annuity due). Then read your result.

What the inputs mean

Starting balance
In payout mode, the payments draw the balance down to exactly zero by the last one. Meanwhile, the money still in the account keeps earning interest.
Annual interest rate
The stated yearly rate. The calculator assumes interest is added as often as you make payments. So with monthly payments, it uses a monthly rate of r ÷ 12, where r is the yearly rate.
Years of payments
Together with the payments per year, this must give a whole number of payments. For example, 2.5 years of quarterly payments is 10 payments, which works.
Payments are made at the
End of period suits most savings plans and loan-style payouts. Start of period suits rent, insurance premiums and withdrawals you take at the start of each month.

Formula and method

i = r ÷ f;  N = f × years
FV = PMT × ((1 + i)^N − 1) ÷ i
PV = PMT × (1 − (1 + i)^(−N)) ÷ i
Payout PMT = PV × i ÷ (1 − (1 + i)^(−N))
Annuity due: FV and PV × (1 + i); payout ÷ (1 + i)

In the formulas, r is the yearly rate as a decimal and f is the number of payments per year. i is the rate for each period, and N is the total number of payments. PMT is the size of each payment, FV is the future value and PV is the present value.

The future value formula adds up every payment, grown with interest to the end of the term. The present value formula does the reverse. It shrinks every payment back to what it's worth today, which is called discounting.

The payout formula is the present value formula, rearranged to find the payment. When payments come at the start of each period, each one gets one extra period of growth, or one less period of discounting. That's where the extra (1 + i) comes from. At a 0% rate, every formula becomes plain multiplication or division by N.

Worked example

You save $500 at the end of every month for 20 years in an account earning 6% a year, compounded monthly.

  1. Rate per month: 0.06 ÷ 12 = 0.005. Number of payments: 12 × 20 = 240.
  2. Future value: $500 × (1.005^240 − 1) ÷ 0.005 ≈ $231,020.45.
  3. You paid in $500 × 240 = $120,000, so about $111,020.45 is interest.
  4. In present value mode, with the same inputs: $500 × (1 − 1.005^(−240)) ÷ 0.005 ≈ $69,790.39.
  5. In payout mode, a $250,000 balance at 6% for 20 years supports about $1,791.08 a month.

Result: Your deposits grow to about $231,020.45. The same series of payments is worth about $69,790.39 today. And $250,000 can pay out about $1,791.08 a month for 20 years.

Understanding the result

Future value answers "how much will I have?" Present value answers "what are these payments worth now?" If someone offers you a lump sum instead of the payments, compare it with the present value. Use a rate you could actually earn.

In payout mode, you receive more in total than the starting balance. That's because the money you haven't withdrawn yet keeps earning interest. The higher the rate, the bigger the payment the balance can keep up.

Assumptions and limitations

  • Payments are all the same size and evenly spaced. The rate stays the same for the whole term.
  • Interest is added once per payment period.
  • In payout mode, the balance falls to exactly zero with the last payment.
  • No fees, taxes or rounding are applied in the calculation.
  • It doesn't handle payments that grow each year, a waiting period before payments begin, or payments for life.
  • This is a math tool, not a quote for an insurance annuity product. Those payouts also depend on fees, life expectancy tables and the insurer's terms.
  • Investment returns are rarely steady. A fixed rate gives a smooth estimate, not a forecast.

Frequently asked questions

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

In an ordinary annuity, payments happen at the end of each period. In an annuity due, they happen at the start. An annuity due has a higher future value and present value, because each payment has one more period to earn interest.

Why is the future value so much larger than the payments I made?

Early payments earn interest for many years, and that interest earns interest too. This snowball effect is called compounding. In the example, $120,000 of deposits grows to about $231,020, because the first deposits grow for almost 20 years.

How do I find out how long a balance will last, instead of the payment?

Use the payout mode and change the years until the payout matches what you plan to withdraw. If the years field offers a solve-for option, you can use that too.

Can I use this for a loan?

Yes. From the lender's side, a loan is an ordinary annuity. In payout mode, enter the loan amount as the balance to get the fixed payment. The loan payment calculator also adds an amortization schedule, a table of how each payment splits between interest and the loan.

How this calculator is checked

Method: Standard future value, present value and capital recovery formulas for ordinary annuities and annuities due. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Annuity Calculator on your own website or blog for free. Paste this code where you want it to appear: