The Term Annuity is Used in Finance Theory to Refer to Any Terminating Stream of Fixed Payments Over a Specified Period of Time

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What is Annuity?

An annuity is an investment that you make, either in a single lump sum or throughinstallments paid over a certain number of years, in return for which you receive back a

specific sum every year, every half-year or every month, either for life or for a fixednumber of years.

After the death of the annuitant or after the fixed annuity period expires for annuitypayments, the invested annuity fund is refunded, perhaps along with a small addition,calculated at that time.

Annuities differ from all the other forms of life insurance discussed so far in onefundamental way - an annuity does not provide any life insurance cover but, instead,offers a guaranteed income either for life or a certain period.

Typically annuities are bought to generate income during ones retired life, which is whythey are also called pension plans. Annuity premiums and payments are fixed withreference to the duration of human life. Annuities are an investment, which can offer anincome you cannot outlive and provide a solution to one of the biggest financialinsecurities of old age; namely, of outliving ones income.

Definition 1A contract soldby an insurance company designed to provide payments to the holderatspecified intervals, usually afterretirement. The holder is taxed only when they starttaking distributions or if they withdraw funds from the account. All annuities are tax-deferred, meaning that the earnings from investments in these accounts grow tax-deferred

until withdrawal. Annuity earnings are also tax-deferred so they cannot be withdrawnwithoutpenalty until a certain specified age. Fixed annuities guarantee a certain paymentamount, while variable annuities do not, but do have the potential for greaterreturns.Both are relatively safe, low-yielding investments. An annuity has a death benefitequivalent to the higher of the current value of the annuity or the amount thebuyerhaspaid into it. If the ownerdies during the accumulation phase, his or herheirs will receive

The term annuity is used in finance theory to refer to any terminating stream of fixedpayments over a specified period of time. This usage is most commonly seen in

discussions of finance, usually in connection with the valuation of the stream ofpayments, taking into account time value of money concepts such as interest rate andfuture value.[1]

Examples of annuities are regular deposits to a savings account, monthly home mortgagepayments and monthly insurance payments. Annuities are classified by payment dates.The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any otherinterval of time.

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Ordinary annuity

An ordinary annuity (also referred as annuity-immediate) is an annuity whosepayments are made at the end of each period (e.g. a month, a year). The values of anordinary annuity can be calculated through the following:[2]

Let:

r= the yearly nominal interest rate.t= the number of years.m = the number of periods per year.i = the interest rate per period.n = the number of periods.

Note:

n = tm

Also let:

P= the principal (or present value).S= the future value of an annuity.R = the periodic payment in an annuity (the amortized payment).

(annuity notation)

Also:

Clearly, in the limit as n increases,

Thus, even an infinite series of finite payments (perpetuity) with a non-zero discount ratehas a finite present value.

Proof

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The next payment is to be paid in one period. Thus, the present value is computed to be:

.

We notice that the second term is a geometric progression of scale factor 1 and of

common ratio . We can write

.

Finally, aftersimplifications, we obtain

.

Similarly, we can prove the formula for the future value. The payment made at the end ofthe last year would accumulate no interest and the payment made at the end of the firstyear would accumulate interest for a total of (n1) years. Therefore,

.

Hence:

.

Additional formula

If an annuity is for repaying a debtPwith interest, the amount owed aftern payments is:

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because the scheme is equivalent with lending an amount and putting part of that, an

amount , in the bank to grow due to interest. See also fixed rate mortgage.

Annuity-due

An annuity-due is an annuity whose payments are made at the beginning of each period.[3] Deposits in savings, rent payments, and insurance premiums are examples of annuitiesdue.

Because each annuity payment is allowed to compound for one extra period, the value ofan annuity-due is equal to the value of the corresponding ordinary annuity multiplied by(1+i). Thus, the future value of an annuity-due can be calculated through the formula(variables named as above):[4]

(annuity notation)

It can also be written as

(1 + i)

An annuity-due with n payments is the sum of one annuity payment now and an ordinaryannuity with one payment less, and also equal, with a time shift, to an ordinary annuitywith one payment more, minus the last payment.

Thus we have:

(Value at the time of the first ofn paymentsof 1)

(Value one period after the time of the lastofn payments of 1)

Other types

Fixed annuities These are annuities with fixed payments. They are primarily used forlow risk investments like government securities or corporate bonds. Fixed annuities offera fixed rate but are not regulated by the Securities and Exchange Commission.

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Variable annuities Unlike fixed annuities, these are regulated by the SEC.They allow you to invest in portions of money markets.

Equity-indexed annuities Lump sum payments are made to an insurancecompany.

Annuity due is useful for lease payment calculations 1

the accumulated amount in the annuity. This money is subject to ordinary income taxes inaddition to estate taxes.

Types of Annuities

Annuities are available in several forms and types, and different annuities havedifferent properties and costs. The properties and costs of annuities are very

important factors that require to be considered properly as business owners puttogether their retirement investment portfolio. Here are a few common types ofannuities defined below.

As the name suggests, an immediate annuity begins providing payouts immediately.The payouts may run either for a specific period or for life, depending on thecontract terms. The immediate annuities that are generally bought with a one-timedeposit, with a minimum of around $10,000 are not very common. This class ofimmediate annuities normally appeals to people who wish to roll over a lump-sumamount from a pension or inheritance and start drawing income from it. Peopleprefer immediate annuities to regular bank accounts because the principal growsmore quickly through annuity investment and because the amount and duration ofpayouts are guaranteed by contract.

On the other hand, a deferred annuity delays payouts until a specific future date. Indeferred annuity the principal amount is invested and allowed to grow tax-deferredover time. Deferred annuities are more common that immediate annuities. Deferredannuities appeal to people who want a tax-deferred investment vehicle in order tosave for retirement.

A fixed annuity offers a guaranteed interest rate over a certain period, usuallybetween one and five years. Fixed annuities are comparable to certificates of deposit(CDs) and bonds, with the main benefit that the sponsor guarantees the return of theprincipal. Fixed annuities generally offer a slightly higher interest rate than CDs andbonds, while the risk is also slightly higher. Additionally, in fixed annuities also theprincipal is allowed to grow tax-deferred until it is withdrawn.

On the other side, a variable annuity offers an interest rate, which changes based onthe value of the underlying investment. Variable annuities are more popular thatfixed annuities. The buyers of variable annuities can usually choose from a range of

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stock, bond, and money market funds for investment purposes in order to diversifytheir portfolios and manage risk. The minimum investment in variable annuitiesusually ranges from $500 to $5,000.

Variable annuities usually feature varying levels of risk, from aggressive growth to

conservative fixed income. In most cases, the annuity principal can be shifted fromone investment to another without being subject to taxation. The variable annuitiesare subject to market fluctuations, however, and investors also must accept a slightrisk of losing their principal if the sponsor company encounters financial difficulties.

Annuity Types?

What Investment Types Are Available?

1. Fixed Annuities

Fixed annuities are invested primarily in high-grade corporate bonds and governmentsecurities. This type offers a guaranteed rate of return, usually in one to ten years.

Types:

A. Market Value Adjustment: The annuity works much like the Guaranteed ReturnAnnuity, below, except there is no guarantee of funds if rates rise and you end orsurrender your contract.

B. The Guaranteed Return: This annuity is a fixed annuity that offers a guarantee that youwill not receive less than 100% of your investment funds. There are no fluctuations in theinterest rate and the market can deplete your initial investment should you surrender yourcontract.

2. Variable Annuities

Variable annuities enable you to invest in specific funds, into sub-accounts. These sub-accounts are tied to the current market's rate.

Types:

Conservative Type:

Money market guaranteed fixed accounts government bonds

Aggressive Type:

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small cap markets funds mid cap markets funds large cap markets funds capital appreciation aggressive growth

emerging markets funds growth markets funds

Special type:

Living benefit annuity

3. Bonus Annuities:

This annuity plan has penalties for early withdrawal but it will also give you a signingbonus up front of 3 to 5%. It's easy to get your money out. The broker simply needs to

agree and reduce their commission in return for you receiving the bonus. This annuitywill need to mature for at least seven years.

Annuity Pay Out Timing:

The next thing to figure out is if you need an immediate or deferred annuity:

A. Deferred Annuities: In a deferred annuity, you receive payments starting at retirement.With a deferred annuity you can invest either a lump sum all at once, or make paymentsover a specified length of time. With Deferred annuities you can invest in either fixed orvariable type accounts. These funds grow tax-deferred until youre ready to begin

receiving funds. Deferred annuities are the most popular type in the US.

B. Immediate Annuities: This is where the investor will start to receive paymentsimmediately upon vesting in the annuity. This annuity is for persons who need immediateincome from an annuity. You can also choose between a fixed payment that doesntchange or a variable payment that is based on the annuity's performance.

Types of Variable Annuities

NonqualifiedNonqualified annuities are purchased with after-tax dollars. This means that when you

are ready to take annuity income payments, you won't owe tax on the portion that'sconsidered return of purchase payments. You only pay taxes on earnings.

There are no government-imposed limits to the amount of money you can contribute toyour nonqualified variable annuity. Your contract will state a date by which you mustbegin to receive annuity income payments, but you may start sooner. Typically, it's aspecific age, usually around age 95 or 100.

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QualifiedAnnuities funding IRAs and qualified plans are typically purchased with pre-tax dollars.

Qualified plans are generally set up by employers for employees under the Internal

Revenue Code for example, 401(k) plans. It's important to know that these plans, aswell as IRAs, are already tax deferred. Therefore, an annuity contract should be used tofund an IRA or qualified plan to benefit from the annuity's features other than taxdeferral. The other benefits of using a variable annuity to fund a qualified plan or an IRAinclude the lifetime income options, guaranteed living and death benefit options and theability to transfer among investment options without sales or withdrawal charges. In fact,Congress has recognized the use of annuity contracts, particularly with respect to fundingIRAs, in the Internal Revenue Code (Section 408(b)).

With a qualified contract or an IRA, when you are ready to retire and take money out,you will owe taxes on both the amount you invested pre-tax and the earnings.

In addition, qualified contracts and IRAs are subject to IRS contribution limits and otherrestrictions.

A fixed annuity is an insurance contract in which the issuing company promises to makefixed dollar payments to the contract holder, the annuitant, for a pre-determined length oftime. In return for payment of the contract premium, the issuing company alsoguarantees both the earnings on the account and the principal balance.

In this article, we're first going to review the fundamental concepts of an annuity. Thenwe're going to talk about the pros and cons of investing in an annuity. Next, we're going

to discuss how fixed annuities work. Finally, we're going to explain some of the featuresyou might find in an annuity contract, including payment terms as well as fees.

Buying Annuities

Most annuities are written contracts issued by life insurance companies. In exchange forpayments of the contract premiums, the contract holder (annuitant) can expect to receivea series of regularly scheduled payments.

Buying an annuity should not be confused withpurchasing life insurance. It's also not asavings account, and it is typically used to supply long-term retirement income. And

because the insurance company guarantees both earnings and principal, the investment isas safe as the financial strength of the insurance company.

Pros and Cons of Annuities

Some of the benefits of annuities are listed below:

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Security - Annuities are considered very safe investments - payments receivedaren't subject to the volatility of the stock market.

Straightforward - After you've bought an annuity, the entire process is simple.Your payment of premiums will guarantee a future source of income.

Stability - Since the contract holder is receiving a fixed monthly payment, it'seasier to create a retirement plan orbudget.

Some of the disadvantages of purchasing an annuity include:

Control - You're paying premiums to the insurance company in exchange for afuture income stream, so you're losing some of the control you'd have if you wereinvesting the money.

Cost - We'll talk more about this later, but under certain conditions, you may notrecover the full benefit of the annuity.

Income Taxes

Annuities offer contract holders the benefit of tax-deferred growth on their money. Forexample, the earnings on the money placed in an annuity grow on a tax-deferred basisuntil withdrawn. By deferring taxes, the contract holder may be able to accumulate moreretirement funds over a shorter period, ultimately providing more retirement income.However, if an annuity contract is surrendered (redeemed), then a tax penalty may applyon surrender.

Fixed Annuity Contracts

When a fixed annuity contract is in its accumulation period, the investment will earn arate of interest as specified by the insurance company. The contract will usually showboth a minimum, or guaranteed, interest rate in addition to a current, or declared interestrate.

The guaranteed interest rate is just that - a minimum rate of interest the contract holderwill earn on their investment that is guaranteed by the insurance company. The current,or declared, interest rate is used by the insurance company to calculate income paymentsin the current period.

As is the case with variable annuities, fixed annuities will typically offer the contractholder options for the way benefits are received, as well as how the premiums are paid.For example, there are:

Immediate or Deferred Annuities, and Single or Installment Premiums

Each of these concepts is explained in the sections below.

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Immediate versus Deferred Annuities

There are two ways the benefits, or payments, are received from an annuity. With animmediate annuity, payments begin shortly after the premium is paid. With a deferredannuity, the income stream is received at a future point in time.

Immediate annuities are used when the contract holder is looking to obtain a steadysource of income immediately. This type of annuity is usually purchased by anindividual looking for a stable source of retirement income.

If the investor is looking for a way to amass money on a tax-deferred basis, then adeferred annuity is chosen. This type of contract allows the annuitant to defer thepayment ofincome tax until the income is needed at a future point in time.

Annuity Premium Payments

Contract holders usually have two options when it comes to making premium paymentson an annuity - single premiums or installment payments. With a single premiumcontract, the annuitant is expected to pay the insurance company one premium.

Installment premiums tend to be associated with more flexible annuity contracts. Thecontract holder might be obligated to make certain minimum payments on a looselydefined schedule. On the other hand, an installment premium might also be defined as avery specific series of payments that are due on a predetermined schedule.

As is the case with any competitive marketplace, different insurance companies will offerfixed annuities at a variety of costs. That being said, the following factors typically

determine the premiums paid on an annuity:

The contract holder's age and gender The payment option selected The size or amount of the annuity purchased The features included in the annuity such as payment guarantees

Features of Fixed Annuity Contracts

The value of any fixed annuity can be calculatedby using premiums paid, subtractingcontract fees or charges, then adding back interest credited to the account. Using thisrelatively simple formula, the insurance company can determine the benefits received bythe contract holder.

Charges or Fees

There are many different charges, or fees, a company may impose as part of the fixedannuity contract. Some annuities are sold with front-loads (which require fees to be paid

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at the start of the contract), while others are back-loaded (which require fees to be paidlater). Finally, a contract might also spread the fees evenly over the life of the annuity.

Buying an annuity is an important decision, so it's vital to understand all of the charges orfees that could affect the premium payments / income benefit. Fixed annuity contracts

may include the following fees / charges:

Percentage of Premium Charge - This charge effectively reduces the value ofthe premiums paid and is usually referred to as a "load." This percentage orpremium charge may diminish over time.

Percentage of Net Assets Charge - Usually associated with variable annuities,the percentage of net assets charge is deducted from the current value of yourannuity. These deductions occur on a predetermined schedule and may occur asfrequently as daily.

Contract Fee - A flat dollar amount that is either a one-time charge or it iscollected as an annual fee.

Transaction Fee - A fixed fee that is paid following each transaction conducted,or premium payment.

Surrender Rights

Most annuity contracts allow the contract holder to surrender the contract if incomebenefits have not yet been received. A contact is terminated when surrendered, and themoney received for the contract is its present value less the surrender fees. Under certainconditions, the amount received at surrender could be less than the amount paid into theannuity.

Surrender Charges

The surrender charge is normally stated as a percentage of the contract's value. In somecases, this percentage will reduce over time and / or as the account's balance grows. Thesurrender charge could also be stated as a reduction in the interest rate.

Annuity Benefits

The last topic we're going to cover is perhaps the most important - the benefits paid by afixed annuity. The income payments are normally received on a monthly basis, althoughit is possible to find payment terms of varying frequencies. As mentioned earlier, the

amount received will depend on factors such as age, gender, contract features, as well asthe contract's value.

The annuity contract itself will contain a table of both guaranteed rates and current rates.These interest rates can be modified by the insurance company at any time. Theguaranteed interest rate will serve as a floor rate - the rate cannot go lower than this level.Generally, there are four types of fixed annuities in the marketplace:

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Life Annuities - Straight life annuities are paid as long as the contract holder isalive. Payments are no longer received after the contract holder passes away.

Term Certain Annuities - With a term-certain annuity, payments are receiveduntil a predetermined date or term. If the annuitant passes away before the term isover, then the insurance company keeps the remaining value of the annuity.

Life With Term Certain Annuities - With this type of annuity, payments arereceived as long as the annuitant is alive. However, if the annuitant should passaway before a "certain period" or term, then a beneficiary will receive paymentfor the remaining term.

Joint and Survivor Annuities - With a joint and survivor annuity, payments arereceived as long as either person named in the annuity is alive.

Free Look Provisions

Laws exist in many states that allow the buyer of an annuity a certain number of days toevaluate the annuity after purchase. If the buyer decides they do not want to keep the

annuity, then they can return the contract and receive a full refund. This type ofarrangement is called a "right to return" or "free look" period.

If the law allows for this free look period, then this feature will be prominently describedin the contract. This is just another reason why it's so important to understand all thefeatures of an annuity before a decision is made to buy a contract.

An Annuity is a bunch of structured payments or equal payments made regularly, likeevery month or every week.

You win the lottery. The lottery guy comes to your house and says you have to choosebetween getting $ 1,000,000 now in one lump sum, or getting structured payments of $50,000 a year for the next 22 years. Which do you take?? Or, similarly, let's say you wereinjured on the job or whatever and were awarded an annuity of structured payments of$50,000 a year for the next 22 years. Perhaps you want to sell your annuity (thepayments) to someone and get a lump sum of cash today. Is it worth $1,000,000?Firstyou have to choose an interest rate. Money is generally worth less in the future, right? Sothat $50,000 payment you get in 22 years is not going to be worth as much as it is today?You know, stuff will be more expensive then, right? So guess an interest rate, in this case,the rate of inflation for the next 22 years. Lets say 4%. Now, you have to figure out whatis the present value of the $50,000 times 22 years discounted by 4% and then compare it

with the million bucks. There are basically 2 ways to do this.

Use a financial calculator. Use an annuity table.

Use a financial calculator - The PV of an Annuity.

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1. Enter n (the number of compounding periods - in this case the number of years).Press 22 and then push the N button.

2. Enter i (the interest rate per period - in this case the number of years). Press 4 andthen push the i button.

3. Enter FV (the future value). It is zero. You want to know the Present Value, not

the future value, right? Push 0 and then push the FV button.4. Enter PMT (the payment). You are not making a payment, you are getting one. Soyou have to show a negative number. Press 50000, then the CHS (change signbutton), then push the PMT button.

5. Push the PV (present value) button.6. Answer = $722,555. This means 22 annual structured payments of 50,000 each is

worth only $722,555 of today's dollars. So you should take the million bucks fromthe lottery guy in one lump sum.

Use an annuity table - The PV of an Annuity.

Somewhere in your book, I bet there is a table that looks something like this:

1% 2% 3% 4%

1 00.9901 00.9804 00.9703 00.9615

2 01.9704 01.9416 01.9135 01.8861

3 02.9410 02.8839 02.8286 02.7751

4 03.9020 03.8077 03.7171 03.6299

5 04.8534 04.7135 04.5797 04.4518

6 05.7955 05.6014 05.4172 05.2421

7 06.7282 06.4720 06.2302 06.0021

8 07.6517 07.3255 07.0197 06.7327

9 08.5660 08.1622 07.7861 07.4353

10 09.4713 08.9826 08.5302 08.1109

11 10.3676 09.7868 09.2526 08.7605

12 11.2551 10.5753 09.9450 09.3851

13 12.1337 11.3484 10.6350 09.9856

14 13.0037 12.1062 11.2961 10.5631

15 13.8651 12.8493 11.9379 11.1184

16 14.7179 13.5777 12.5611 11.6523

17 15.5623 14.2919 13.1661 12.1657

18 16.3983 14.9920 13.7535 12.6593

19 17.2260 15.6785 14.3238 13.1339

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20 18.0456 16.3541 14.8775 13.5903

21 18.8570 17.0112 15.4150 14.0292

22 19.6604 17.6580 15.9369 14.4511

1. Find this table.2. On the left, find the number of compounding periods (in this case years) - 223. On the top, find the interest rate - 4%4. Find below where they meet. It says 14.45115. Multiply 14.4511 times the Payment - $50,0006. Answer = $722,555. This means 22 annual structured payments of 50,000 each is

worth only $722,555 of today's dollars. So you should take the million bucks fromthe lottery guy in one lump sum.

Each payment of an ordinary annuity belongs to the payment periodprecedingits date,while the payment of an annuity-due refers to a payment periodfollowingits date.

The meaning of the above statement may not be immediately obvious until we look at itgraphically...

A more simplistic way of expressing the distinction is to say that payments made underan ordinary annuity occur at the end of the period while payments made under an annuitydue occur at the beginning of the period.

A third possibility is to define an annuity due in terms of an ordinary annuity: anannuity-due is an ordinary annuity that has its term beginning and ending one period

earlier than an ordinary annuity. This definition is useful because this is how we willcompute an annuity due; i.e., in relation to an ordinary annuity (discussed further in"Calculating the Value of an Annuity Due" below).

Most annuities are ordinary annuities. Installment loans and coupon bearing bonds areexamples of ordinary annuities. Rent payments, which are typically due on the daycommencing with the rental period, are an example of an annuity-due.

Note that an ordinary annuity is sometimes referred to as an immediate annuity, which isunfortunate because it implies that the payments are made immediately (i.e., at thebeginning of the period, which would be the case with an annuity-due). However,ordinary annuity is the more widely used term.

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2. Calculating the Value of an Annuity Due

An annuity due is calculated in reference to an ordinary annuity. In other words, tocalculate either the present value (PV) or future value (FV) of an annuity-due, we simply

calculate the value of the comparable ordinary annuity and multiply the result by a factorof(1 + i) as shown below...

Annuity Due = Annuity Ordinary x (1 + i)

This makes sense because if we go back to our earlier definitions we see that thedifference between the ordinary annuity and the annuity due is one compounding period.

Note also that the above formula implies that both the PV and the FV of an annuity duewill be greater than their comparable ordinary annuity values. This is illustratedgraphically in the section that follows, "Visual Comparison of Cash Flows." It can also be

clearly seen in the discount and accumulation schedules constructed in the "Excel"section.

The following examples illustrate the mechanics of the ordinary annuity calculation andsubsequent annuity due calculation.

a. Present Value of an Annuity

Using the example problem from the Present Value of an Annuity page, we calculate thePV of an ordinary annuity of $50 per year over 3 years at 7% as...

...and the present value of an annuity due under the same terms is calculated as...

...and just as we thought, the PV of the annuity due is greater than the PV of the ordinaryannuity; by 9.18 in this example.

b. Future Value of an Annuity

Using the example problem from the Future Value of an Annuity page, we calculate theFV of an ordinary annuity of $25 per year over 3 years at 9% as...

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...and the future value of an annuity due under the same terms is calculated as...

...and again the FV of the annuity due is greater than the FV of the ordinary annuity; inthis example by 7.38.

3. Visual Comparison of Cash Flows

The distinction between an ordinary annuity and an annuity-due can be easily grasped byvisualizing the timing of the payments.

a. Present Value of an Annuity:

Ordinary Annuity. Continuing with the same example from the Present Value of anAnnuity page, the following illustration shows how payments are applied in the case of

an ordinary an nuity:

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Annuity-Due. With an annuity-due the payments are made at the beginning rather thanthe end of the period...

Note that the PV of the ordinary annuity is 131.22 and the PV of the annuity-due is140.40 (calculated as 131.22 x 1.07).

The fact that the value of the annuity-due is greater makes sense because all the paymentsare being shifted back (closer to the start) by one period. This means the PV should belarger under the annuity due because all the payments are made earlier. In other words,they are all closer to the "present" so they are subject to less discounting. Note that thereis no need to discount the first payment under the annuity due at all; since it is made atthe very outset, its PV is its face value.

b. Future Value of an Annuity:

Continuing with the same example from the Future Value of an Annuity page, thefollowing illustration shows how payments are applied in the case of an ordinaryannuity...

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Annuity-Due. With an annuity-due the payments are made at the beginning rather thanthe end of the period.

Note that the FV of the ordinary annuity is 81.95 and the FV of the annuity-due is 89.33(calculated as 81.95 x 1.09).

The fact that the value of the annuity-due is greater makes sense because all the paymentsare being shifted back (closer to the start) by one period. Moving the payments backmeans there is an additional period available for compounding. Note the under theannuity due the first payment compounds for 3 periods while under the ordinary annuity

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it compounds for only 2 periods. Likewise for the second and third payments; they allhave an additional compounding period under the annuity due. The additionalcompounding generates a largerFV.

4. Example Problems

The following solved problems illustrate the distinction between an ordinary annuity andan annuity due.

QID 7. At 5% annual interest, what is the difference in the present value of $100 paid atthe end of each year for 10 years and $100 paid at the beginning of each year?

This problem calculates the difference between the present value (PV) of an ordinary

annuity and an annuity due. The timing difference in the payments is illustrated in anExcel schedule.

QID 32. You plan to deposit $100 into a savings account at the end of each month for thenext 5 years. a) At 3% compounded monthly, how much will you have accumulated atthe end of 5 years? b) How much difference would it make if the payments were made atthe beginning of the month rather than at the end?

This problem calculates the amount to which a monthly payment will grow over time

(i.e., the FV) assuming payments are made 1) at the end of each month; and 2) the

beginning of each month. The discussion includes an Excel accumulation schedule andgraphics showing how the annuity due calculation is specified in the Excel FV function

and the HP-12C calculator ([g][BEG]).