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Present value of an annuity: Formula, calculator, and examples

Ever wonder what a series of future payments is worth right now? The present value (PV) of an annuity tells you exactly that, converting future payments into today’s dollars. In this guide, we’ll cover the PV annuity formula and walk you through examples of how these calculations work. 

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What’s the present value of an annuity?

The PV of an annuity shows you what future payments are worth today after applying a discount rate. This reflects the time value of money — the idea that money available now can earn interest and grow faster than money you receive later. To calculate the PV of an annuity, you need to know:

• Payment amount: How much money you receive for every annuity payment
• Payment frequency: How often the annuity pays (monthly, quarterly, or yearly)
• Number of payments: The total payments you’re scheduled to receive
• Discount rate: The rate used to adjust future payments to today’s value, heavily influenced by inflation and interest rates 

When is the present value of an annuity useful?

The PV of an annuity is useful anytime you need to compare future payments to money you could invest today. It turns a stream of payments into a single number so it’s easier to evaluate trade-offs and choose between different financial options.

PV to compare lump sum vs. annuity payouts

PV is a big help when comparing a lump-sum payment and ongoing annuity payments. By converting future payments into today’s dollars, PV lets you see whether the annuity is worth more than the upfront amount. This comparison is common with pensions and structured settlements.

PV for retirement income planning

In retirement planning, PV helps you understand the real value of guaranteed income streams. You can use it to judge annuities against other investments or decide when steady income outweighs growth potential. PV also makes it easier to align income choices with your risk tolerance. 

PV in loan/insurance/settlement valuation

Lenders, insurers, and legal professionals often use PV to price contracts and settlements. It helps quantify the value of payment schedules in insurance benefits and legal settlements, ensuring future payouts reflect current interest rates.

Ordinary annuity vs. annuity due

The main difference between an ordinary annuity and an annuity due is when you get paid. Ordinary annuities pay at the end of the period, while an annuity due pays at the beginning. 

Receiving money sooner means you can reinvest it faster, so payments made earlier (annuity due) are generally worth more than those received later. 

How present value changes

Annuity due payments happen at the beginning of each period rather than at the end, meaning they’re worth more today than an equivalent ordinary annuity. That extra time allows for an additional period of compounding. You can convert between them using the formula:

PVdue = PVord x (1 + r) 

This formula works for any discount rate (r) and any periods.

Timeline illustration

Here’s how payment timing differs between these two.

Ordinary annuity: 

Period 1 ── Period 2 ── Period 3 ── Period 4

      $PMT   $PMT $PMT         $PMT

Annuity due:

$PMT         $PMT       $PMT   $PMT

Period 0 ── Period 1 ── Period 2 ── Period 3

That one-period shift forward is why an annuity due always produces a higher present value, even when the payment amount and number of periods stay the same.

Present vs. future value of annuity

PV and future value (FV) are similar, but understanding both helps you make informed decisions.

Present value of an annuity

PV tells you what future payments are worth today by factoring in the time value of money plus opportunity cost. Use it to compare annuity options or decide between a lump sum and multiple payouts.

The annuity formula for present value is:

PV = PMT × (1 − (1 + r)^−n) / r

• PMT = payment per period
• r = discount rate per period
• n = number of payments

Keep in mind, this formula is for an ordinary annuity and assumes constant interest rate and fixed payment intervals.

You can apply this when evaluating the present worth of a future income stream or deciding whether to take a lump-sum payment versus spread payments over time.

Future value of an annuity

FV projects how much payments or contributions will grow by a specific date, accounting for compound interest. Use it when planning for long-term goals or estimating growth during the contribution phase.

The annuity formula for future value is:

FV = PMT × ((1 + r)^n − 1) / r

• PMT = payment per period
• r = discount rate per period
• n = number of payments

This formula is for an ordinary annuity and assumes a compound interest rate. You can apply this when estimating how much your annual contributions will grow over 10, 20, or 30 years, or for calculating potential returns during the accumulation period.

How discounting works

Discounting is based on the idea that getting paid now is better than getting paid later because money held today can be invested.

To figure out what a future payment is worth right now, you can divide the amount by (1+r) for every period you have to wait. Money arriving soon is worth a lot more than the same amount arriving years down the road.

Common mistakes to avoid

• Mixing annual/monthly inputs: Convert rates and periods so they match.
• Miscounting periods: Confirm the total number of payments for the annuity.
• Forgetting the annuity type: The formula assumes an ordinary annuity, but annuities due require a (1+r) adjustment.

How to calculate the present value

You can calculate the present value in a few different ways, depending on how comfortable you are with the math and how precise you need it to be.

Use the PV of an annuity formula 

The most direct method is to use the formula introduced above. It gives you visibility into how each variable helps you see how each part affects the outcome. It also works well if you want to double-check the math. 

You’ll plug in the payment amount, discount rate per period, and number of periods. Then you calculate PV manually or with a present value of the annuity calculator. 

Use a PVIFA table/chart

The present value of an annuity formula is built around the present value interest factor of an annuity (PVIFA). PVIFA tables show the discount factors for common interest rates and time periods. Instead of computing the full formula, you find the PVIFA value that matches your rate and number of periods, then multiply it by the payment amount.

PV of annuity charts are helpful, but they work best when your inputs align with the table values.

Use Excel or a calculator

Spreadsheets and online calculators are the fastest way to compute present value. Excel and Google Sheets have a built-in PV function that handles the math for you. This is ideal when stress-testing assumptions or working with longer time horizons. Just be careful to match payment timing and compounding frequency so the results are accurate.

PVIFA explained

PVIFA is a shortcut for present value calculations. Rather than discounting payments one at a time, PVIFA rolls the time value of money into a single factor you can multiply by that payment amount.

What PVIFA is and why it simplifies PV 

PVIFA represents the combined effect of (1) interest rates and (2) time on a series of equal payments. By using just one multiplier, you avoid repeating the same discounting steps for every payment period.

When rates increase, PVIFA decreases because future payments are discounted more heavily. When the number of periods increases, PVIFA rises because you’re receiving more payments overall. 

PVIFA formula

PVIFA captures how time and the discount rate affect a series of equal payments. It lets you calculate present value with a single multiplier instead of discounting payments individually.

PV = PMT × PVIFA 

PVIFA = (1 - (1 + r)^-n) / r

• PV = the total value of all annuity payments
• PMT = the fixed payment made each period
• r = the discount or interest rate per period
• n = the total number of payment periods

PVIFA increases when payments arrive over more periods and decreases as the discount rate rises, which directly affects present value.

How to read a PVIFA table

To use a PVIFA table, find the column that matches your discount rate and the row that matches your number of periods. The value at their intersection is the PVIFA. Multiply that factor by payment amount to estimate present value. 

Examples of how to calculate the present value of annuities

These step-by-step scenarios show how to calculate present value and apply it to real financial decisions.

Retirement income stream

Say you’re evaluating a retirement annuity that pays $1,000 per year for 5 years, starting at the end of each year. The discount rate is 5% annually, and payments follow an ordinary annuity structure. 

Step 1: Identify the variables

• PMT = $1,000
• r = 0.05
• n = 5

Step 2: Write the formula

PV = PMT × (1 − (1 + r)^−n) / r

Step 3: Plug in the values

PV = 1,000 × (1 − (1.05)^−5) / 0.05

Step 4: Calculate

PV = 1,000 × 4.32948 = 4,329.48

The present value of the retirement income stream is $4,329.48. 

Here’s an Excel/Sheets formula for that amount:

=PV(0.05, 5, 1000, 0, 0)

Structured settlement vs. lump-sum choice

Say you’re deciding between taking a lump sum right now or receiving $1,000 a year for the next 5 years. Because that first $1,000 check arrives immediately, this counts as an annuity due, which is slightly more valuable than if you had to wait until year-end to get paid.

Step 1: Use the ordinary annuity PV

PV = 1,000 × (1 − (1.05)^−5) / 0.05 = 4,329.48

Step 2: Adjust for annuity due

PVdue​ = PVord​ × (1+r)

Step 3: Plug in the values

PVdue ​= 4,329.48 × 1.05

Step 4: Calculate

PVdue = 4,545.95

The present value of the annuity due is $4,545.95. 

Here’s an Excel/Sheets formula for that amount:

=PV(0.05, 5, 1000, 0, 1)

How accurate is the present value calculation?

The accuracy of PV calculations comes down to your discount rate and compounding schedule.

Picking a discount rate

The discount rate has a big impact on present value. A higher rate lowers PV, whereas a lower rate raises it. If you’re comparing a lump sum to annuity payments, it’s important to test multiple rates against their opportunity costs and inflation to determine the true, risk-adjusted value of future payments.

Compounding frequency

Present value calculations assume a specific compounding schedule. Annual, monthly, and daily compounding can produce different results — even with the same stated interest rate. 

To keep your calculations accurate, you’ll need to match the compounding frequency to the payment schedule and convert rates as necessary.

Lifetime annuities can’t be ideally PV’d

You can’t calculate present value for a lifetime annuity without estimating how long payments will last. But because most PV calculations use a fixed time horizon, they’re better for comparing options than they are for predicting total lifetime value.

Team up with Gainbridge for retirement planning

If you’re ready to turn present value math into real retirement decisions, explore Gainbridge. You can compare annuity rates and see how different payout timelines affect what your income is worth now. Use our calculator to model options that fit your goals.

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This article is for informational purposes only. It is not intended to provide, and should not be interpreted as, individualized investment, legal, or tax advice. The Gainbridge® digital platform provides informational and educational resources intended only for self-directed purposes.

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