In the last section you learned about annuities. In an annuity, you start with nothing, put money into an account on a regular basis, and end up with money in your account.

In this section, we will learn about a variation called a **Payout Annuity**. With a payout annuity, you start with money in the account, and pull money out of the account on a regular basis. Any remaining money in the account earns interest. After a fixed amount of time, the account will end up empty.

Payout annuities are typically used after retirement. Perhaps you have saved $500,000 for retirement, and want to take money out of the account each month to live on. You want the money to last you 20 years. This is a payout annuity. The formula is derived in a similar way as we did for savings annuities. The details are omitted here.

Payout Annuity Formula

(P=frac{wleft(1-left(1+frac{r}{k} ight)^{-k t} ight)}{left(frac{r}{k} ight)})

(P) is the balance in the account at the beginning (starting amount, or principal).

(w) is the regular withdrawal (the amount you take out each year, each month, etc.)

(r) is the annual interest rate (in decimal form. Example: (5\% = 0.05))

(k) is the number of compounding periods in one year.

(t) is the number of years we plan to take withdrawals

Like with annuities, the compounding frequency is not always explicitly given, but is determined by how often you take the withdrawals.

When do you use this

Payout annuities assume that you __take__ money from the account __on a regular schedule (every month, year, quarter, etc.)__ and let the rest sit there earning interest.

Compound interest: __One__ deposit

Annuity: __Many__ deposits.

Payout Annuity: __Many withdrawals__

Example 1

After retiring, you want to be able to take $1000 every month for a total of 20 years from your retirement account. The account earns 6% interest. How much will you need in your account when you retire?

**Solution**

In this example,

(egin{array} {ll} w = $1000 & ext{the monthly withdrawal} r = 0.06 & 6\% ext{ annual rate} k = 12 & ext{since we’re doing monthly withdrawals, we’ll compound monthly} t = 20 & ext{ since were taking withdrawals for 20 years} end{array})

We’re looking for (P); how much money needs to be in the account at the beginning.

Putting this into the equation:

[ egin{align*} P& =frac{1000left(1-left(1+frac{0.06}{12} ight)^{-20(12)} ight)}{left(frac{0.06}{12} ight)} P &=frac{1000 imesleft(1-(1.005)^{-240} ight)}{(0.005)} P &=frac{1000 imes(1-0.302)}{(0.005)}=$ 139,600 end{align*}]

You will need to have $139,600 in your account when you retire.

Notice that you withdrew a total of $240,000 ($1000 a month for 240 months). The difference between what you pulled out and what you started with is the __interest earned__. In this case it is ($ 240,000-$ 139,600=$ 100,400) in interest.

Evaluating negative exponents on your calculator

With these problems, you need to raise numbers to negative powers. Most calculators have a separate button for negating a number that is different than the subtraction button. Some calculators label this [(-)], some with [+/-] . The button is often near the = key or the decimal point.

If your calculator displays operations on it (typically a calculator with multiline display), to calculate (1.005^{-240})you'd type something like: (1.005 [wedge ] [(-)] 240)

If your calculator only shows one value at a time, then usually you hit the [(-)] key after a number to negate it, so you would hit: (1.005 ; [ ext{y}^ ext{x}] ; 240 ; [(-)] =)

Give it a try - you should get (1.005^{-240}=0.302096)

Example 2

You know you will have $500,000 in your account when you retire. You want to be able to take monthly withdrawals from the account for a total of 30 years. Your retirement account earns 8% interest. How much will you be able to withdraw each month?

**Solution**

In this example,

We’re looking for d.

(egin{array} {ll} r = 0.08 & 8\% ext{ annual rate} k = 12 & ext{since we’re doing monthly withdrawals} t = 30 & ext{ since were taking withdrawals for 30 years} P = $500,000 & ext{we are beginning with }$500,000 end{array})

In this case, we’re going to have to set up the equation, and solve for (w).

[ egin{align*} 500,000 &=frac{wleft(1-left(1+frac{0.08}{12} ight)^{-30(12)} ight)}{left(frac{0.08}{12} ight)} 500,000 &=frac{wleft(1-(1.00667)^{-360} ight)}{(0.00667)} 500,000 &=w(136.232) w &=frac{500,000}{136.232}=$ 3670.21end{align*}]

You would be able to withdraw $3,670.21 each month for 30 years.

Excercise 1

A donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?

**Answer**(egin{array} {ll} w = ext{ unknown} & r = 0.04 & 4\% ext{ annual rate} k = 1 & ext{since we’re doing annual scholarships} t = 20 & ext{ since were taking withdrawals for 20 years} P = $100,000 & ext{we are starting with } $100,000 end{array})

[100,000=frac{wleft(1-left(1+frac{0.04}{1} ight)^{-20 imes 1} ight)}{frac{0.04}{1}} onumber]

Solving for (w) gives $7,358.18 each year that they can give in scholarships.

It is worth noting that usually donors instead specify that only interest is to be used for scholarship, which makes the original donation last indefinitely. If this donor had specified that, ($100,000(0.04) = $4,000) a year would have been available.

Important Topics of this Section

Find the present value of an annuity (principal required)

Find the payments that can be made from a payout annuity

## The ABCs of annuities: 6 questions to ask

(MoneyWatch) Guaranteed income for life, especially in the aftermath of a deep recession and financial crisis, sounds wonderful. That must be why insurance companies are ramping up their marketing of annuities. Due to the complexity of annuities, I'll cover the basics in this post, and then set forth the pros and cons in the following one.

An annuity is a financial contract issued by a life insurance company that offers tax-deferred savings and a choice of payout options (income for life, income for a certain period of time or lump sum) to meet your needs in retirement. Because the contract enjoys tax-deferred treatment, the IRS may impose a 10 percent early withdrawal penalty for some distributions if they are taken before age 59 1/2.

The concept of trading a lump sum of money for a stream of income is easy to understand, but annuities come in lots of flavors, which can make them confusing. The two big categories of annuities are "immediate" and "deferred."

In an immediate annuity, payments begin immediately or within one year of the policy's issue. These contracts are also referred to as "single premium immediate annuities" or SPIAs because they are usually purchased with a single deposit. SPIAs can help you manage the risk of outliving your money, which is known as "longevity risk."

A deferred annuity has two phases: the accumulation phase, during which your money grows on a tax-deferred basis and the payout phase, during which you begin to receive scheduled payments. There are several types of deferred annuities to consider:

-- Fixed annuity: Insurance companies guarantee a fixed interest rate for a certain period of time. At the end of this period, the company will declare a renewal interest rate and another guarantee period. Most guarantee a minimum interest rate for the life of the contract.

### Trending News

-- Variable annuity: For investors who want access to more investment options, variable annuities offer "sub-accounts," which look like mutual funds inside of an insurance policy.

-- Equity index annuity: A blend between a fixed and a variable, where the insurance company invests in a mix of bonds and stocks designed to return a targeted percentage of a particular index (e.g., S&P 500). The owner does not control the investment selection but can participate to a degree in stock market gains during a rising market. Conversely, if markets fall, the contract guarantees a minimum return, typically three percent.

When an insurance salesman, a financial adviser or a broker broaches the topic of annuities with you, here are six questions that you should immediately ask:

1. What type of annuity is this, and why do you recommend it for me?

2. Exactly how much will I pay in the first year of the contract, and then how much in subsequent years?

3. What will be your first-year commission on the contract, and what will you earn in subsequent years? Annuities are notoriously expensive (more on the fees in next week's column), so you will want to understand the total costs, which include mortality and expense charges ("M&E"), administrative fees, underlying fund expenses, charges for special features and the salesperson's commission.

4. Have I already maxed out other tax-deferred vehicles? One of the big selling points of annuities is that they offer tax deferral. That's great, but make sure that you are maximizing your 401(k) or IRA accounts first before investing in an annuity, because chances are, those are cheaper tax-deferred vehicles.

5. Should I tie up my money with this contract? Once you sign up for an annuity, it's hard to get your hands on that money, and it can be expensive to do so. Make sure you have ample liquidity outside of the annuity before taking the plunge.

6. "How is this insurer rated by AM Best, S&P, Moody's and Fitch?" Before the financial crisis, this question seemed silly, but now we know that insurance companies can go broke. Since the success of an annuity is predicated on the survival of the insurance company, it's important that the company be highly rated.

Distributed by Tribune Media Services, Inc.

First published on July 20, 2012 / 10:09 AM

© 2012 CBS Interactive Inc. All Rights Reserved.

View all articles by Jill Schlesinger on CBS MoneyWatch »

Jill Schlesinger, CFP®, is the Emmy-nominated, Business Analyst for CBS News. She covers the economy, markets, investing and anything else with a dollar sign on TV, radio (including her nationally syndicated radio show), the web and her blog, "Jill on Money." Prior to her second career at CBS, Jill spent 14 years as the co-owner and Chief Investment Officer for an independent investment advisory firm. She began her career as a self-employed options trader on the Commodities Exchange of New York, following her graduation from Brown University.

## Period Certain vs. Guaranteed Lifetime Payments

After selecting either a deferred or immediate annuity, you must consider how long you wish to receive payouts from the insurer.

Annuities can provide guaranteed income for life — or for a certain period of time. They may also offer money to your beneficiary after you die.

Two popular payout options are life and period certain.

### Guaranteed Lifetime Payments

Life annuities, as the name implies, pay out for the rest of your life. They may also be called single life, life only or straight life.

This option helps protect against longevity risk, or the threat of outliving your money in retirement.

This protection is increasingly relevant as a growing number of Americans report inadequate retirement savings.

According to Northwestern Mutual’s 2020 Planning & Progress Study, 22 percent of Americans have less than $5,000 saved for retirement — and 36 percent of respondents said they don’t know how much they have saved.

The amount of a life annuity payout is determined by how much you invest and your life expectancy.

Life annuities do not guarantee money for your heirs or spouse after you pass away.

### Period Certain

Period certain annuities only guarantee payments for a specific amount of time. It’s like term life insurance, which only provides coverage for a set number of years.

If you die before the end of your contract period, your beneficiary receives the rest of your payments for the remaining period.

Period certain annuities do not hedge against longevity risk.

## Special Considerations

An annuity is a financial product that pays a fixed stream of payments to an individual. It is primarily used by retirees as a form of guaranteed income.

Annuities are created and sold by financial institutions, which invest funds deposited by individuals over time, and then when the client is ready, begin issuing regular payments drawn from the account to the annuity holder.

The period of time when an annuity is being funded and before payouts begin is referred to as the accumulation phase. Once payments begin, the contract is in the annuitization phase.

Annuities are appropriate for individuals seeking stable, guaranteed retirement income. Because the money invested in the annuity is not accessible without a penalty, it is not recommended for younger people or those who don't have an emergency fund that they can tap into if necessary.

## $6.3 million settlement: did annuity expire with Pt?

CASE FACTS: In 2004, Kathleen Bernath brought a medical malpractice suit against Frankford Hospital-Bucks County, Frankford Healthcare System, Inc., Jefferson Health System, Inc., and Frankford Hospitals. Her suit was for medical malpractice for injuries sustained following surgery at Frankford Hospital. In 2005, she entered into a written settlement agreement with the defendants. The parties agreed that the settlement agreement was tantamount to a general release. Frankford Hospital issued a check payable to Bernath in the amount of $4,239,890. It also issued a $1,660,000 check to New York Life for the annuity agreed upon as part of the settlement which called for paying Bernath $20,000 per month for life. However, within two weeks after the check for the annuity was sent to New York Life, Bernath died. After a trial, the trial court ordered New York Life to pay Bernath's Estate $1.660,000. The trial court held the obligation to pay the annuity arose when the parties entered into the agreement. Accordingly, the trial court ruled that the $1,660,000 was due and payable to Bernath's estate. The insurer appealed. The Superior Court affirmed the judgment entered by the trial court. It found that the duty to pay the $1.6 million to obtain an annuity was not stipulated upon an event but arose when the contract was executed. The court believed that the insurer recognized the obligation to pay the $1.6 million by sending the check to New York Life to purchase the annuity, and would not have contracted to pay the $20,000 per month annually themselves because Bernath 'might' have remained alive for many years, costing more than the agreed upon amount. The Superior Court concluded that changed circumstances, which made it impossible for the purchase of the agreed upon annuity. The Superior Court found that the form of the obligation changed following death, and the estate was owed $1.66 million to satisfy the $6.3 million "total consideration." Thus the Superior Court of Pennsylvania rendered judgment ordering New York Life to return the $1.66 million dollars premium paid to it. However, New York Life, insisting that it had taken a risk pursuant to which it could have been obligated to pay Bernath $20,000 per month for life, and had she lived to a ripe old age it may have found itself paying out far more than it had received in the premium paid for the purchase of the annuity. Accordingly, New York Life appealed.

COURT'S OPINION: The Supreme Court of Pennsylvania reversed the order of the lower court. The court held, inter alia that the defendants had no threshold obligation to pay $5.9 Million to Bernath, but to directly pay her $4,239,890 and $20,000 per month, with the option to assign that duty to New York Life by buying an annuity for $1.6 million. The court concluded that the fact that annuity contract was not executed prior to Bernath's death was not material since the unambiguous language of the settlement agreement terminated the periodic payments upon death. Since Bernath did not agree to receive a $1.6 million lump sum, but rather $20,000 per month to end upon her death, the defendants were found not to be obligated to provide Bernath's estate with what Bernath herself did not bargain for. Thus, the court concluded that the defendants were entitled to recoup the money sent to New York Life.

LEGAL COMMENTARY: The court prefaced its decision by noting that settlement agreements are governed by contract law principles. When a written contract is clear and unequivocal, its meaning must be determined by its contents alone. It speaks for itself and a meaning cannot be given to it other than that expressed. Where the intention of the parties is clear, there is no need to resort to extrinsic aids or evidence. Hence, where language is clear and unambiguous, the focus of interpretation is upon the terms of the agreement as manifestly expressed, rather than as, perhaps silently intended. Having reviewed the plain language of the settlement agreement, the court could not agree that it was ever the parties' intention that Bernath receive a total payment of $ 6.3 Million. Accordingly, the court concluded that it could not agree that New York Life pay $1.6 million to Bernath's estate. The court observed that if the hospital had chosen not to exercise its right to purchase the annuity, it was precisely same. Had the hospital opted instead to pay out of its own pocket, Bernath's Estate would have no claim to the $1.6 million because the language of the contract clearly stated the periodic payments would cease upon Bernath's death. The court found that this was of vital importance since it was precisely the situation in which the parties found themselves at the time of Bernath's death. The responsible party had the duty to fund the periodic payments out of its own pocket until death.

## Low Interest Rates Will Sink Your Annuity Payout

When interest rates are low, payouts from annuities are depressed, too. Payouts are usually tied to rates for 10-year Treasuries, and that rate is historically low. If you’re worried that interest rates could go lower—or you’d like to start receiving at least some guaranteed income now—**consider building an annuity ladder**. With this strategy, you spread the amount you want to invest in an immediate annuity over several years. For example, if you want to invest $200,000, you would buy an annuity for $50,000 this year and another $50,000 every two years until you have spent the entire amount. If rates rise, you’ll be able to capture them, and if they fall, you’ll have locked in payments at the higher rate.

## A 6.3% Dividend From Apple? Here’s How.

Tech stocks have finally taken a breather—and we’re going to pounce on this dip—and grab a rare “double discount” while we’re at it.

The strategy we’re going to use also lets us “squeeze” the biggest tech names for payouts that are unheard of in the sector—I’m talking yields up to 6.3%.

**Mom’s Coupon-Clipping Goes High-Tech**

This approach is an ode to my mom who, to this day, refuses to pay the sticker price. If there’s a coupon to be found, she’ll find it *and* find another coupon to secure a double discount—even if it requires management approval to apply!

The dividend equivalent of the back-to-back coupon is buying discounted closed-end funds (CEFs) after a pullback, and that’s exactly the setup we’ve got in tech now.

To see what I’m getting at, consider **Apple AAPL (AAPL).** As I write this, the stock is off about 10% this year and 16% from the all-time high it hit on January 26.

Here’s where our “extra” discount comes in, because when you buy Apple through a CEF that’s *also* trading at a discount, you get an even better deal (and that big dividend I mentioned a second ago, too).

### These 3 REIT Dividends Benefit From Inflation

### These 3 Funds Make $300K Last Forever

### Delta Variant Could Push U.S. Covid Immunity To 85%, Says Former FDA Head

Case in point: the **Columbia Seligman Premium Technology Growth Fund (STK).** Apple is the CEF’s No. 2 holding, at 5.5% of the portfolio. And, thanks to the selloff, STK has traded at discounts to net asset value (NAV) as wide as 4% in the last few days, and this discount is narrowing as I write this. That’s down from the premium at which the fund usually trades.

(In other words, the fund trades for *less than the value of its portfolio,* a quirk that exists only with CEFs. The bottom line is that a CEF’s share price can, and often does, trade below its portfolio’s value—setting up a disconnect we can pounce on.)

We can thank the panic over rising interest rates—and the consequent selloff in tech stocks—for this sale on STK, which really opened up in the past couple weeks.

So what kind of upside can we expect as a result?

Besides the appreciation of its (oversold) portfolio of tech names—which includes not only Apple but heavyweights **Microsoft MSFT (MSFT)** and **Alphabet (GOOGL)—**we can look forward to an additional pop from STK’s closing “discount window.”

Consider that this fund has traded at a 1.23% premium, on average, in the past 12 months. Just a return to that level (a no-brainer, in my opinion), would give a few percentage points of “head start” upside from the closing discount alone.

But keep in mind that this 1.24% premium is just the average over the last year: STK’s share price has jumped as much as *12.6% above of its portfolio value*. A return to a premium like that would drive discount-driven price gains of 15%! (To be honest, I think STK will land somewhere in the middle, between the average and all-time high premiums, as tech inevitably rebounds.)

**Dividend Sweetens the Deal Further**

The best thing (besides the discounts!) about buying CEFs is their outsized dividends. STK yields 6.3%, *nine times* more than Apple’s meager 0.68% payout and *nearly seven times* greater than Microsoft’s 1% dividend.

That makes our tech strategy simple: buy the dip now, double up our deal with a CEF trading at a discount, then collect our dividends as that “discount window” eases shut. When the discount flips to a premium, or when that premium goes above the long-term average, we sell and roll our gains into *another* discounted CEF.

**Another Tech CEF to Watch Now—and (Maybe) Rotate Into Later**

STK isn’t your only option in tech CEFs. Another one to pay close attention to is the **BlackRock Science and Technology Trust (BST).**

BST’s portfolio looks a lot like that of STK, with a lean toward Big Tech firms like Apple, Microsoft and **Amazon.com (AMZN),** but also a weighting toward payment processors—which are vital in our quasi-self-isolated economy—such as **Visa V (V), Mastercard MA (MA)** and **PayPal (PYPL).**

The fund *does* yield less than STK, with a 4.2% payout, but it makes up for that by paying monthly instead of quarterly, and it’s steadily raised its dividend since inception in 2014, to the tune of 87% (with two special dividends thrown in for good measure)!

What’s more, BST has outperformed STK on a total-return basis (including dividends and share-price gains) since inception.

The only snag is that BST’s quality is no secret: as I write this, the fund trades at a 4.7% premium to NAV, which is well above the 0.8% average premium at which it’s traded over the past year.

That high premium will likely cap BST’s upside as tech bounces back, making STK the better choice now. BST is a good fund to keep an eye on, though, and potentially roll into once its premium falls back to a discount.

*Brett Owens is chief investment strategist for* *Contrarian Outlook**. For more great income ideas, get your free copy his latest special report:* Your Early Retirement Portfolio: 7% Dividends Every Month Forever.

## How is the PV of Annuity Formula derived?

The present value of a series of payments, whether the payments are the same or not, is

When the periodic payments or dividends are all the same, this is considered a geometric series. By using the geometric series formula, the formula can be rewritten as

This equation can be simplified by multiplying it by (1+r)/(1+r), which is to multiply it by 1. Notice that (1+r) is canceled out throughout the equation by doing this. The formula is now reduced to

The P's in the numerator can be factored out of the fraction and become 1. The 1's in the denominator of the formula are subtracted from one another. After making these adjustments, the formula is simplified to the present value of annuity formula shown on the top of the page.

## 3 Year Fixed Annuity Rates | Highest Current Rates Three Year Annuities

Below you will find the highest current interest rates and product guidelines for 3 year multi-year guaranteed annuities (MYGA). MYGA's are fixed annuities that are commonly referred to as CD-Type annuities. You can read a detailed description of multi-year guaranteed annuities here. MYGA's guarantee a fixed rate of return for the entire duration of the contracts, typically ranging from 3 to 10 years. The key distinction between a MYGA and other types of fixed annuities is the term of the guaranteed rate. A MYGA annuity's rate is guaranteed for the full contract term. Other types of fixed annuities still offer a guaranteed rate, though it may only be for a portion of the term.

**Annuity rates can change daily. Receive the most up-to-date rates by requesting The MYGA Report with the form below.**

**Select a specific contract length, or choose all years to view the highest rates for each term.**

#### Call 1-800-501-1984 for purchase options.

American Life American Classic 3 (MVA) | 3 yrs. | $1,000 | 2.25% | B++ |

Oceanview Harbourview 3 (MVA) | 3 yrs. | $20,000 | 2.25% | A- |

Liberty Bankers Life Bankers Elite 3 (MVA) | 3 yrs. | $10,000 | 2.15% | B++ |

American National Palladium MYG 3 High-Band (MVA) | 3 yrs. | $250,000 | 2.10% | A |

Guggenheim Life and Annuity Preserve MYGA 3 High-Band (MVA) | 3 yrs. | $250,000 | 2.10% | B++ |

Sagicor Milestone MYGA 3 High-Band (MVA) | 3 yrs. | $100,000 | 2.05% | A- |

Guggenheim Life and Annuity Preserve MYGA 3 Low-Band (MVA) | 3 yrs. | $10,000 | 2.00% | B++ |

American National Palladium MYG 3 Low-Band (MVA) | 3 yrs. | $100,000 | 1.95% | A |

Fidelity & Guaranty FG Guarantee-Platinum 3 Annuity (MVA) | 3 yrs. | $20,000 | 1.95% | A- |

Delaware Life Pinnacle MYGA 3 (MVA) | 3 yrs. | $10,000 | 1.80% | A- |

American Equity GuaranteeShield 3 (MVA) | 3 yrs. | $10,000 | 1.75% | A- |

Midland National Life Guarantee Ultimate 3 High-Band (MVA) | 3 yrs. | $100,000 | 1.75% | A+ |

North American Guarantee Choice 3 High-Band (MVA) | 3 yrs. | $100,000 | 1.75% | A+ |

Mass Mutual Stable Voyage 3 (MVA) | 3 yrs. | $100,000 | 1.65% | A++ |

Oxford Life Multi-Select 3 (MVA) | 3 yrs. | $20,000 | 1.60% | A- |

New York Life Secure Term MVA II 3 High-Band (MVA) | 3 yrs. | $100,000 | 1.55% | A++ |

Equitrust Life Certainty Select 3 (MVA) | 3 yrs. | $10,000 | 1.50% | B++ |

Sagicor Milestone MYGA 3 Low-Band (MVA) | 3 yrs. | $50,000 | 1.50% | A- |

Mass Mutual Stable Voyage 3 (MVA) | 3 yrs. | $10,000 | 1.40% | A++ |

Midland National Life Guarantee Ultimate 3 Low-Band (MVA) | 3 yrs. | $10,000 | 1.30% | A+ |

North American Guarantee Choice 3 Low-Band (MVA) | 3 yrs. | $10,000 | 1.30% | A+ |

Minnesota Life SecureOption Choice 3 High-Band (MVA) | 3 yrs. | $100,000 | 1.15% | A+ |

Minnesota Life SecureOption Choice 3 Low-Band (MVA) | 3 yrs. | $25,000 | 1.00% | A+ |

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