# PV Formula of Annuity: Present Value Guide & Examples

Published: 2026-04-19
Author: Warren Team
URL: https://www.heywarren.com/blog/pv-of-annuity-formula

---
A lottery winner hits a $30 million jackpot, paid as $1 million per year for 30 years. The "lump sum" cash buyout? Around $15 million — half the headline number. Most people assume the lottery is cheating them, but the math is honest. The pv formula of annuity tells you exactly why future dollars are worth less than today's dollars, and it values everything from pensions and mortgages to lease payments and retirement income streams. Knowing the present value of annuity formula cold is what separates real financial literacy from rough-cut intuition that costs people millions in bad decisions.

This guide walks through the formula step by step, with worked examples you can replicate in Excel or on paper. We'll cover ordinary annuities versus annuities due, sensitivity to discount rates, perpetuities, growing annuities, and the most common mistakes people make. By the end, you'll evaluate pension lump-sum offers, mortgage payoffs, and bond prices using the same toolkit a CFA charterholder uses on day one. No black boxes, no hand-waving — just the formula, the intuition, and the practical mechanics.

## What Is an Annuity in TVM Terms?

In time value of money (TVM) language, an annuity is a stream of equal, periodic payments made at fixed intervals. Think monthly mortgage payments, annual pension checks, or quarterly bond coupons. The defining features are equal payment size (PMT), equal time gaps, and a finite number of periods (n).

### Ordinary annuity vs annuity due

An ordinary annuity pays at the end of each period. Most bonds and mortgages work this way. An annuity due pays at the beginning of each period — rent and [insurance premiums](/blog/what-are-insurance-premiums) are classic examples. The timing difference seems small, but it shifts present value by a factor of (1+r), which adds up over long horizons.

### Why annuities matter for valuation

Almost every long-term financial product is an annuity in disguise. Your $2,000 monthly mortgage is a 360-payment annuity. A $50,000 annual pension is a multi-decade annuity. Even a Treasury bond's coupon stream is an annuity layered on top of a single bullet repayment at maturity.

## PV Formula of Annuity Explained

The present value of annuity formula discounts every future payment back to today and sums them up. Rather than calculating each cash flow separately, the formula collapses the geometric series into one clean equation, saving you from running 360 separate discount calculations on a 30-year mortgage.

![How the present value annuity formula transforms a stream of future payments into a single lump-sum value today.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20660%20125%22%20width%3D%22660%22%20height%3D%22125%22%20role%3D%22img%22%3E%3Ctitle%3EFlow%20diagram%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%2230%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22115%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPMT%3C%2Ftext%3E%3Ctext%20x%3D%22115%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3Epayment%20per%20period%3C%2Ftext%3E%3Cline%20x1%3D%22205%22%20y1%3D%2262.5%22%20x2%3D%22237%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22244%2C62.5%20235%2C57.5%20235%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22245%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22330%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPVAF%3C%2Ftext%3E%3Ctext%20x%3D%22330%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3E%5B%281%E2%88%92%281%2Br%29%5E%E2%88%92n%29%2Fr%5D%3C%2Ftext%3E%3Cline%20x1%3D%22420%22%20y1%3D%2262.5%22%20x2%3D%22452%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22459%2C62.5%20450%2C57.5%20450%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22460%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22545%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPV%3C%2Ftext%3E%3Ctext%20x%3D%22545%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3Elump-sum%20today%3C%2Ftext%3E%3C%2Fsvg%3E)

*How the present value annuity formula transforms a stream of future payments into a single lump-sum value today.*

For an ordinary annuity:

PV = PMT × [(1 − (1+r)^(-n)) / r]

For an annuity due, multiply the result by (1+r):

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

Where:
- PMT = payment per period (in dollars)
- r = periodic interest rate (as a decimal)
- n = number of periods

The bracketed term `[(1 − (1+r)^(-n)) / r]` is called the present value annuity factor, or PVAF. It represents the present value of receiving $1 per period for n periods at rate r. Multiply that factor by your actual payment, and you have the lump-sum value today.

### The intuition behind the formula

Each future payment is worth less than face value because you could invest a smaller amount today and grow it to that future amount. The discount factor `(1+r)^(-n)` shrinks payment n. Summing the geometric series of these shrinking weights gives you the bracketed expression — a closed-form shortcut for an otherwise tedious sum.

### Periodic vs annual rate

If your stated interest rate is annual but payments are monthly, divide by 12. A 6% annual rate becomes a 0.5% monthly rate, and n becomes 12 times the number of years. Mismatching frequency between rate and periods is the single most common source of error in annuity calculations.

## Worked Examples Using the PV of Annuity Formula

Concrete numbers cement the concept. The first example shows a textbook case; the second tackles the lottery scenario from the intro and reveals why the "cash option" looks so much smaller than the advertised jackpot.

### Example 1: $1,000 per year for 10 years at 5%

Plug into the ordinary annuity formula:

PV = 1,000 × [(1 − (1.05)^(-10)) / 0.05]
PV = 1,000 × [(1 − 0.6139) / 0.05]
PV = 1,000 × [0.3861 / 0.05]
PV = 1,000 × 7.7217
PV ≈ $7,722

So $10,000 of nominal future payments is worth about $7,722 today at a 5% discount rate. The $2,278 gap is the time value cost of waiting.

### Example 2: $30 million lottery, $1M per year for 30 years

The lottery's headline figure is $30M, but the cash option uses a higher discount rate to account for the state's investment [opportunity cost](/blog/formula-of-opportunity-cost). Here's how PV moves with the rate:

| Discount rate | PV of $1M × 30 years |
|---|---|
| 3% | $19.60M |
| 4% | $17.29M |
| 5% | $15.37M |
| 6% | $13.76M |
| 7% | $12.41M |

At 5% — a typical long-term Treasury proxy — the present value is about $15.4M, which closely matches real-world lump-sum offers. The state isn't ripping you off; they're paying you the actuarial fair value. The "missing" $15M is just discounting at work.

## PV of Annuity: Ordinary vs Due

The single difference between ordinary and annuity due is timing. Ordinary annuities pay at period-end, and annuity due pays at period-start. Because annuity due payments arrive one period earlier, each one is discounted one less period, making the total present value higher by exactly a factor of (1+r).

![Annuity due PV is 5% higher than ordinary annuity for $1,000/year over 10 years at 5%.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20210%22%20width%3D%22800%22%20height%3D%22210%22%20role%3D%22img%22%3E%3Ctitle%3EComparison%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Ctext%20x%3D%22230%22%20y%3D%2257.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EOrdinary%20Annuity%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%2225%22%20width%3D%22428.5767143561914%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22680.5767143561914%22%20y%3D%2257.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%232563eb%22%3E%247.7K%3C%2Ftext%3E%3Ctext%20x%3D%22230%22%20y%3D%22152.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EAnnuity%20Due%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%22120%22%20width%3D%22450%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%237c3aed%22%2F%3E%3Ctext%20x%3D%22702%22%20y%3D%22152.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%237c3aed%22%3E%248.1K%3C%2Ftext%3E%3C%2Fsvg%3E)

*Annuity due PV is 5% higher than ordinary annuity for $1,000/year over 10 years at 5%.*

### When to use each convention

Use ordinary annuity for bonds, mortgages, car loans, and most fixed-income securities. Use annuity due for rent, insurance premiums, lease payments, and any contract where you pay upfront. Pension payments vary — read the contract before assuming.

### A quick comparison

For $1,000/year for 10 years at 5%:
- Ordinary annuity PV: $7,722
- Annuity due PV: $7,722 × 1.05 = $8,108

The $386 difference seems trivial, but on a $1M/year pension, it's $386,000 in your pocket. Always confirm timing before signing.

## Why the Discount Rate Matters

The discount rate is the lever that controls everything. Higher r means lower PV, because future dollars get discounted more aggressively. Small rate changes produce surprisingly large valuation swings, especially over long horizons — a 1% rate move on a 30-year stream can shift PV by 10% or more.

### Sensitivity table for $1,000/year over 20 years

| r | PV |
|---|---|
| 2% | $16,351 |
| 4% | $13,590 |
| 6% | $11,470 |
| 8% | $9,818 |
| 10% | $8,514 |

Notice that PV nearly halves as the rate moves from 2% to 10%. This is why retirees obsess over interest rates: the present value of their future spending and pension income is intensely rate-sensitive.

### Picking the right rate

Use the opportunity cost of capital — what you could earn elsewhere with comparable risk. For pension valuation, long-term Treasury yields plus a small risk premium are common. For corporate cash flows, [weighted average cost of capital](/blog/how-to-calculate-weighted-cost-of-capital) (WACC) is standard. Never use a CD rate to value a 30-year stream; it understates risk and inflates PV.

## Excel Implementation: The PV Function

Excel's built-in PV function automates the math. The syntax is `=PV(rate, nper, pmt, [fv], [type])`, where rate is the periodic rate, nper is the number of periods, and pmt is the payment per period. The fv (future value) and type arguments are optional.

### Sign convention quirk

The Excel PV function returns a negative number by design. Excel treats cash outflows as negative and inflows as positive, so a stream of incoming PMT values produces an outgoing lump-sum equivalent. Wrap the formula in `-PV(...)` or pass a negative PMT to get a positive result.

### Worked Excel example

For Example 1 above, type:

`=PV(0.05, 10, -1000)` → returns $7,721.73

For an annuity due, set type=1:

`=PV(0.05, 10, -1000, 0, 1)` → returns $8,107.82

Always check whether your model uses end-of-period (type=0, default) or beginning-of-period (type=1) payments.

## Real-World Applications

The pv formula of annuity isn't an academic exercise — it underpins most consumer and corporate finance decisions. Once you internalize it, you start seeing annuities everywhere, and you stop accepting headline numbers at face value.

### Mortgage valuation

Your monthly payment times the PV annuity factor equals the loan principal. A $2,398/month payment for 360 months at 0.5% monthly rate (6% APR) gives PV = $2,398 × 166.79 = $400,000 — exactly the mortgage you signed for. Refinancing math runs the same calculation in reverse.

### Pension lump sum vs annuity decision

When your employer offers $500,000 lump sum or $30,000/year for life, the PV formula tells you the breakeven discount rate. If your personal opportunity cost is below that breakeven, take the annuity. If it's higher, take the lump sum and invest it.

### Lease vs buy

Discount the lease payment stream at your borrowing rate and compare to the asset's purchase price. If the lease PV exceeds the purchase price, buying is cheaper in present-value terms. This is how fleet managers and CFOs make leasing calls.

### Bond pricing

A bond's price equals the PV of its coupon annuity plus the PV of its face value at maturity. For a 10-year, 5% coupon bond at 4% yield: price = (PV of $50/year for 10 years at 4%) + ($1,000 / 1.04^10) = $405.55 + $675.56 = $1,081.11.

### Retirement income planning

To find how much capital you need for $60,000/year for 30 years at 4% real return, compute PV: $60,000 × 17.29 = $1.04M. That's your retirement number — derived directly from the PV of annuity formula.

## Special Cases: Perpetuity and Growing Annuity

Two important variations extend the basic formula. A perpetuity has infinite payments, and a growing annuity has payments that increase at a constant rate. Both show up frequently in valuation work, especially for stocks, real estate, and inflation-linked income streams.

![The four main annuity types used in valuation, each a variation on the core PV formula.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20760%20211%22%20width%3D%22760%22%20height%3D%22211%22%20role%3D%22img%22%3E%3Ctitle%3EHierarchy%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%22300%22%20y%3D%2220%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22380%22%20y%3D%2254%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22white%22%3EAnnuity%20Types%3C%2Ftext%3E%3Cpath%20d%3D%22M%20380%2078%20L%20380%20105.5%20L%20110%20105.5%20L%20110%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%2230%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22110%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EOrdinary%3C%2Ftext%3E%3Ctext%20x%3D%22110%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3Eend-of-period%3C%2Ftext%3E%3Cpath%20d%3D%22M%20380%2078%20L%20380%20105.5%20L%20290%20105.5%20L%20290%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22210%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22290%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EAnnuity%20Due%3C%2Ftext%3E%3Ctext%20x%3D%22290%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3Estart-of-period%3C%2Ftext%3E%3Cpath%20d%3D%22M%20380%2078%20L%20380%20105.5%20L%20470%20105.5%20L%20470%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22390%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22470%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPerpetuity%3C%2Ftext%3E%3Ctext%20x%3D%22470%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EPMT%20%2F%20r%3C%2Ftext%3E%3Cpath%20d%3D%22M%20380%2078%20L%20380%20105.5%20L%20650%20105.5%20L%20650%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22570%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22650%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EGrowing%3C%2Ftext%3E%3Ctext%20x%3D%22650%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EPMT%20grows%20at%20g%3C%2Ftext%3E%3C%2Fsvg%3E)

*The four main annuity types used in valuation, each a variation on the core PV formula.*

### Perpetuity formula

When n approaches infinity, the formula collapses to:

PV = PMT / r

A $1,000 annual perpetual payment at 5% is worth $1,000 / 0.05 = $20,000. British "consol" bonds and preferred stock dividends are real perpetuity examples. The formula is also the engine behind the Gordon Growth Model in equity valuation.

### Growing annuity formula

When payments grow at rate g per period:

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

Useful for inflation-adjusted pensions or salary streams. If r = g, the formula breaks (division by zero), and PV simplifies to n × PMT / (1+r). Always check that r > g before applying.

## Common Mistakes to Avoid

Even finance professionals trip over these errors. Most stem from sloppy unit conversion or assumption mismatches. A quick checklist before you trust any annuity output saves real money.

### Wrong period count

If payments are monthly and you use annual n, your PV will be off by a factor of 12. Always count actual payment periods, not years.

### Mixing nominal and real rates

If your PMT grows with inflation, use a real (inflation-adjusted) discount rate. If PMT is fixed nominal dollars, use a nominal rate. Mixing them inflates or deflates PV by the inflation rate compounded over n periods.

### Ordinary vs annuity due confusion

Always confirm payment timing. An annuity due valued as ordinary understates PV by a factor of (1+r) — meaningful on long-dated streams.

### Ignoring FV of annuity

The PV formula has a sibling, the FV of annuity formula: FV = PMT × [((1+r)^n − 1) / r]. Use FV when you want to know what a savings stream grows into; use PV when you want today's lump-sum equivalent.

## Authoritative Sources

For deeper background and primary-source data on this topic, the following authoritative sources are useful starting points:

- [IRS Retirement Plans](https://www.irs.gov/retirement-plans)
- [Social Security Administration](https://www.ssa.gov/)
- [U.S. Department of Labor — EBSA](https://www.dol.gov/agencies/ebsa)

## Conclusion

The pv formula of annuity is one of the highest-leverage tools in personal finance. Five takeaways to lock in:

1. PV = PMT × [(1 − (1+r)^(-n)) / r] for ordinary annuities; multiply by (1+r) for annuity due.
2. The discount rate is the master lever — small rate changes cause large PV swings on long-dated streams.
3. Always match rate frequency to payment frequency (monthly rate with monthly periods).
4. Use Excel's `=PV(rate, nper, pmt)` to automate, and remember the sign convention returns a negative number.
5. Perpetuities collapse to PMT/r; growing annuities adjust the denominator to (r − g).

Master these and you can value mortgages, pensions, bonds, leases, and retirement income with the same toolkit a CFA uses on day one. As interest rates fluctuate over the coming decade, your ability to translate payment streams into present values will be the single biggest determinant of whether you make sound capital allocation decisions or get fooled by big-sounding headline numbers.

Ready to put this knowledge to work? Try Warren, your AI financial advisor — get personalized, conflict-free guidance at heywarren.com

---


## Related Reading

**More from Warren**:
- [Future Value of an Annuity: Formula, Examples, and How to Calculate It](/blog/future-value-annuity)
- [Using a 401(k) for a Home Purchase: Rules, Costs, and Alternatives](/blog/401k-used-for-home-purchase)
- [Deferred Annuity: How It Works and Whether It's Right for You](/blog/deferred-annuities)

**Authoritative sources**:
- [IRS — Retirement Plans](https://www.irs.gov/retirement-plans)
- [Department of Labor — Retirement](https://www.dol.gov/general/topic/retirement)
- [IRS Publication 590-A — Contributions to IRAs](https://www.irs.gov/pub/irs-pdf/p590a.pdf)