Annuity Calculator

At the most basic level, an annuity is a series of equal payments made at regular intervals. Those intervals could be monthly, quarterly, or annually. The key variables are always the same: the payment amount, the number of periods, and the interest rate per period.

The interest rate is what makes an annuity more interesting than a simple savings plan. Because money earns interest over time, a dollar today is worth more than a dollar a year from now. Annuity calculations account for that time value of money in every formula.

There are two broad directions you can calculate in. You can work forward, asking what your payments will grow into by some future date. Or you can work backward, asking what a stream of future payments is worth right now. Those two directions are called future value and present value, and they're covered in detail below.

Insurance companies, pension funds, and banks all use annuity math constantly. So do mortgage lenders, since a mortgage is really just an annuity in reverse. You borrow a lump sum and repay it through a series of equal monthly payments over time.

The future value of an annuity tells you how much a series of regular deposits will be worth at some point in the future, assuming each payment earns interest from the moment it's made. This is the number most people care about when they're building savings.

Say you deposit $200 every month into an account earning 6% annual interest. After 20 years, you haven't just saved $48,000. Each deposit has been compounding, so the total is significantly higher. The future value formula captures all of that growth.

The formula for the future value of an ordinary annuity (where payments happen at the end of each period) is:

FV = PMT × [((1 + r)ⁿ − 1) / r]

• FV = future value of the annuity
• PMT = payment amount per period
• r = interest rate per period
• n = total number of payment periods

If payments are made at the beginning of each period instead, you multiply the result by (1 + r) to get the annuity due future value. That one adjustment can add up to a meaningful difference over many years.

The present value of an annuity flips the question around: instead of asking what your payments will grow into, you're asking what a stream of future payments is worth in today's dollars. This matters a lot when you're evaluating pension offers, settlement options, or any situation where someone promises you a series of payments down the road.

The logic is simple. A payment you'll receive five years from now is worth less than the same payment today, because money you have today can earn interest in the meantime. Present value discounts those future payments back to the present using an interest rate, often called the discount rate.

The formula for the present value of an ordinary annuity is:

PV = PMT × [(1 − (1 + r)⁻ⁿ) / r]

• PV = present value of the annuity
• PMT = payment amount per period
• r = discount rate per period
• n = number of payment periods

This calculation is used all the time in bond pricing, lease agreements, and retirement planning. If someone offers you a lump sum today versus a series of monthly payments over 10 years, present value math tells you which option is actually worth more.

Sometimes you already know the total amount you're working with, and you need to figure out what the regular payment should be. That's what an annuity payment calculator does. It's especially useful for loan repayment planning, where you know the loan balance and want to know the monthly payment, or for retirement planning, where you know your target nest egg and want to know what monthly income it can support.

The payment formula is derived directly from the present value formula, just solved for PMT:

PMT = PV × [r / (1 − (1 + r)⁻ⁿ)]

If you're calculating payments based on a future value target instead, the formula rearranges from the future value equation:

PMT = FV × [r / ((1 + r)ⁿ − 1)]

Plug in your numbers and you get the payment size that makes everything balance out. Mortgage calculators, car loan estimators, and retirement income planners are all running some version of this formula behind the scenes. The inputs look different depending on the context, but the underlying math is the same.

The difference between an ordinary annuity and an annuity due comes down to timing. In an ordinary annuity, payments happen at the end of each period. In an annuity due, payments happen at the beginning. That one shift changes the math slightly but consistently.

Because annuity due payments come in one period earlier, each payment has more time to earn interest. That makes the future value higher compared to an ordinary annuity with identical inputs. The adjustment is straightforward: take any ordinary annuity result and multiply it by (1 + r) to convert it to annuity due.

Most loan payments are ordinary annuities. Rent and subscription payments are usually annuity due, since you pay at the start of each month or year. Knowing which type you're dealing with keeps your calculations accurate.

A retirement annuity calculator is really a combination of the tools already described, applied to one of the most important financial questions most people face: will I have enough money, and how long will it last?

There are two common scenarios people use this for. The first is accumulation, where you're still working and want to know what your monthly contributions will grow into by retirement. The second is distribution, where you've already got a lump sum saved and want to figure out how much you can withdraw each month without running out of money.

For the accumulation phase, you use the future value formula. For the distribution phase, you're essentially solving for the payment using the present value formula, treating your retirement savings as the present value and calculating how long it can support a given monthly withdrawal.

A few things worth keeping in mind when running retirement annuity calculations:

• Use a realistic interest rate. The stock market has historically averaged around 7% after inflation over the long run, but you may want to use a more conservative number for planning purposes.
• Adjust for inflation. A $3,000 monthly payment sounds comfortable today, but it'll have less purchasing power 20 years from now.
• Account for taxes. Withdrawals from traditional retirement accounts are taxed as ordinary income, which reduces the effective payment you actually take home.
• Consider the time horizon carefully. Underestimating how long you'll live is one of the most common and costly mistakes in retirement planning.

Many people combine a personal annuity calculation with Social Security estimates to get a clearer picture of total retirement income. Running the numbers yourself first, before talking to a financial advisor, puts you in a much stronger position to ask the right questions.

All annuity calculations share the same core inputs, just arranged differently depending on what you're solving for. Here's a consolidated look at the key formulas:

One thing to watch closely is keeping your rate and period consistent. If payments are monthly, use the monthly interest rate (annual rate divided by 12) and count periods in months, not years. Mixing annual rates with monthly periods is one of the most common errors people make when running these calculations by hand.

Spreadsheet software like Excel or Google Sheets has built-in functions for all of these: FV(), PV(), and PMT(). They're handy for quick calculations, though understanding the underlying formula helps you catch mistakes and interpret the results correctly.

Seeing the formulas in action makes them a lot easier to work with. Here are a few practical examples that cover common scenarios.

Example 1: Future Value of Monthly Savings

You contribute $300 per month to a retirement account earning 6% annual interest (0.5% per month) for 30 years (360 months).

FV = 300 × [((1.005)³⁶⁰ − 1) / 0.005]
FV = 300 × [(6.0226 − 1) / 0.005]
FV = 300 × 1,004.52
FV ≈ $301,354

You contributed $108,000 out of pocket. The rest is interest. That's the power of compounding over time.

Example 2: Present Value of a Pension

You're offered a pension that pays $1,500 per month for 20 years (240 months). Using a discount rate of 5% annually (0.4167% per month), what's that stream of payments worth today?

PV = 1,500 × [(1 − (1.004167)⁻²⁴⁰) / 0.004167]
PV = 1,500 × [(1 − 0.3691) / 0.004167]
PV = 1,500 × 151.53
PV ≈ $227,295

If someone offers you a lump sum buyout of less than $227,295, the monthly pension is the better deal at that discount rate.

Example 3: Monthly Mortgage Payment

You borrow $250,000 at 7% annual interest (0.5833% per month) for 30 years (360 months).

PMT = 250,000 × [0.005833 / (1 − (1.005833)⁻³⁶⁰)]
PMT = 250,000 × [0.005833 / 0.8757]
PMT ≈ $1,663 per month

Over 30 years, you'd pay roughly $598,680 total. The difference between that and the original $250,000 loan is what the lender earns in interest. These kinds of calculations are worth running before you sign any long-term financial agreement.