## Annuity

## Sell Your Annuity

Do you have annuity you dont want? Discover When is it Time to Sell Your Annuity? What can I do? Where can I get the money I need? I have an annuity, but I dont know that I can sell it. Is there a good time to sell my annuity? I already have a home improvement loan, but it was used before the roof needed replacing.

## Non Standard Annuities and Gradients

As discussed in Section 3.3, the standard assumption for annuities and gradients is that the payment period and compounding period are the same. If they are not, the formulas given in this chapter cannot be applied directly. There are three methods for dealing with this situation 1. Treat each cash flow in the annuity or gradient individually. This is most useful when the annuity or gradient series is not large. 2. Convert the non-standard annuity or gradient to standard form by changing the compounding period. 3. Convert the non-standard annuity to standard form by finding an equivalent standard annuity for the compounding period. This method cannot be used for gradients. Figure 3.9 Non-Standard Annuity for Example 3.9 Method 1 Consider the annuities as separate future payments. Method 3 Convert the annuity to an equivalent yearly annuity. This can be done by considering the first payment as a future value over the first four-year period, and finding the equivalent annuity over that...

## Compound Interest Factors for Annuities

The next four factors involve a series of uniform receipts or disbursements that start at the end of the first period and continue over N periods, as illustrated in Figure 3.2. This pattern of cash flows is called an annuity. Mortgage or lease payments and maintenance contract fees are examples of the annuity7 cash flow pattern. Annuities may also be used to model series of cash flows that fluctuate over time around some average value. Here the average value would be the constant uniform cash flow. This would be done if the fluctuations were unknown or deemed to be unimportant for the problem. Figure 3.2 Annuity Over N Periods The series present worth factor, denoted by (P A,i,N), gives the present amount, P, that is equivalent to an annuity with disbursements or receipts in the amount, A, where the interest rate is and the number of periods is .V. It is the reciprocal of the capital recovery factor

## Present Value Of An Annuity

Suppose that you were offered the following alternatives a 3-year annuity of 1,000 per year or a lump-sum payment today. You have no need for the money during the next 3 years, so if you accept the annuity, you would simply deposit the receipts in a savings account paying 4 interest. How large must the lump-sum payment be to make it equivalent to the annuity The time line shown in Figure A.4 will help explain the problem. The present value of the first receipt is R 1 (1 + i) , the second is R 1 (1 + i) 2, and so on. Designating the present value of an annuity of n years as An and the present value interest factor for an annuity as PVIFAin, we may write the following equation

## Annuities

The second type of cash flow stream that lends itself to a quick formula is an annuity, which An Annuity pays the stop after T periods. For example, if the interest rate is 10 per period, what is the value of an years' annuity that pays 5 per period for 3 periods (1+r) (1+r)2 (1+r)3 The annuity formula makes short work of this NPV calculation, Is this really a short-cut Maybe not for 3 periods, but try a 360-period annuity, and let me know which method you prefer. Either works.

## Annual percentage rate of interest

Where t is the number of years of the loan. annuity (G0) An amount of money paid annually or at other regular intervals. Major examples include life assurance premiums, pensions, rent payments and instalment payments. An annuity certain has a fixed term, unlike a perpetuity whose payments continue indefinitely (e.g. an unredeemable government stock). An annuity contingent depends on an uncertain event, e.g. the death of a person. The purchase price, or present value V, of an annuity depends on the rate of interest used in the calculation where i is the rate of interest (expressed as a decimal) and n is the number of periods that the annuity is paid.

## Present Worth PW and Annual Worth AW Comparisons

Another way to look at the project is to suppose that, once Steve has set up the network off campus, he tries to sell it. If he can convince potential investors, who demand a return of 20 a year, that the expectation of a S30 000 per year cash flow for five years is accurate, how much would they be willing to pay for the network Investors would calculate the present worth of a 20 annuity paying 30 000 for five years. This is given by Annual worth comparisons are essentially the same as present worth comparisons, except that all disbursements and receipts are transformed to a uniform series at the MARR, rather than to the present worth. Any present worth P can be converted to an annuity A by the capital recovery factor (A P,i,N). Therefore, a comparison of two projects that have the same life by the present worth and annual worth methods will always indicate the same preferred alternative. Note that, although the method is called annual worth, the uniform series is not necessarily on a...

## Present Value Analysis and the Difficulty of Forecasting Future Cash Flow

A perfect business in terms of the simplicity of valuation would be an annuity an annuity generates an annual stream of cash that either remains constant or grows at a steady rate every year. Real businesses, even the best ones, are unfortunately not annuities. Few businesses occupy impenetrable market niches

## Perpetuities And Capitalized Costs

A perpetuity is an annuity in which the periodic payments continue indefinitely. This type of annuity is of particular interest to engineers, for in some cases they may desire to determine a total cost for a piece of equipment or other asset under conditions which permit the asset to be replaced perpetually without considering inflation or deflation.

## Economic and environmental analysis

Within the scope of the economic analysis, power generation costs will be calculated for the discussed types of solar thermal power plants. In line with the preceding assessment method, applied throughout this book, the costs for construction and operation are determined and distributed in the form of annuities over the technical lifetime of the power plant. On the basis of these annual amortisation costs and the provided electric energy, the electricity generation costs per kilowatt hour are calculated. If not otherwise indicated, a technical lifetime of 25 years for all machine equipment and an interest rate of 4.5 have been assumed to allow for a comparison with other power generation options.

## PAi5 PAi5 500160 3125

An alternative way to get the IRR for this problem is to convert all cash outflows and inflows to equivalent annuities over the five-year period. This will yield the same result as when present worth was used. Annuity equivalent to the disbursements 500(A P,i*,5) Annuity equivalent to the receipts 160 Again, setting the two equal,

## Prices and Present Values

Conversely, some individuals wish to convert a fixed sum of money into a stream of future payments. Elderly people who are retiring with what seems like an adequate amount to live on must be concerned with whether they will live longer than expected-outlive their money as the expression goes and end up in poverty. In order to avoid this, they may use a portion of their money to purchase an annuity from an insurance company. For example, as of the year 2001, by purchasing an annuity for 100,000, a seventy year old man would receive 772 a month for life-whether that life was three more years or thirty more years. In other words, the risk would be shifted to the insurance company, for a price. As in other cases, the risk is not only shifted but reduced, since the insurance company can more accurately predict the lifespan of millions of people to whom it has sold annuities than any given individual can predict his own lifespan. Incidentally, a woman aged 70 would get somewhat smaller...

## Compound Interest Factors for Discrete Compounding

A set of equal disbursements or receipts over a sequence of periods, referred to as an annuity 3. Annuities and gradients coincide with the ends of sequential periods. (Section 3.8 suggests several methods for dealing with annuities and gradients that do not coincide with the ends of sequential periods.)

## The Marginal Efficiency Of Capital

The relation between the prospective yield of a capital asset and its supply price or replacement cost, i.e. the relation between the prospective yield of one more unit of that type of capital and the cost of producing that unit, furnishes us with the marginal efficiency of capital of that type. More precisely, I define the marginal efficiency of capital as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price. My italics in this sentence. This gives us the marginal efficiencies of particular types of capital-assets. The greatest of these marginal efficiencies can then be regarded as the marginal efficiency of capital in general.

## On Commerce and Luxury

Body of the nation were in such profound ignorance of this important secret that we had neither minister nor magistrate that knew what the words annuities, principal, exchange, or dividend meant. It was destined that a Scotchman called John Law2 should come into France and overturn the whole economy of our government to instruct us. He had the courage, in the most horrible confusion of our finances, and in the time of a most dreadful famine, to establish a bank and an India company. This was giving a vomit to the sick we took too much, and convulsions were the consequence but, at length, from the ruins of his system, we had left us an India company, with a capital amounting to the sum of fifty millions of livres. What had been the case had we taken a moderate dose of that salutary medicine In my opinion, the state had certainly been the most vigorous and powerful in the whole world.

## Example Two False Efficiency

Lorenzen retired as planned, he would have received the entire lump sum.24 However, under S & H's plan, when employees died before retiring, their spouses were entitled only to 40 percent of what the lump sum would have been (if the lump sum was selected) or to 50 percent of the monthly annuity payments (if the '50 percent joint-and-survivor' plan was selected).25 Mrs. Lorenzen sued the plan program for a violation of fiduciary duties to her husband and herself.26 She claimed that S & H did not adequately appraise her husband of the risks of his electing to keep on working rather than to retire at the earliest opportunity. Specifically, S & H did not warn him that delaying retirement would cut his retirement benefits in half if he died before retirement.27 Furthermore, the spousal consent form, which she signed, did not warn her that she would not receive the full lump sum if her husband died before retiring.28

## State Earnings Related Pension Scheme

When reviewed in 1985, SERPS was criticized for its costs, for not targeting on the needy, for giving too large a role to the state and for discouraging private schemes. it was initially proposed then to replace the scheme with the requirement that at least 4 per cent of earnings be contributed to an occupational or private scheme to purchase an annuity subsequently this was modified to the recommendation to reduce contributions by setting pension levels lower so that they would only replace 20 per cent of employment earnings.

## Social Security Reform

A further issue in the design of a pensions system is the choice between a defined contributions system and a defined benefits system. In a defined contribution scheme, social security contributions are paid into an investment fund and, at the time of retirement, the accumulated fund is annuitized. What annuitized means is that the fund purchases an annuity which is a financial instrument that pays a constant income to the purchaser until their date of death. In a defined benefits scheme, contributions are made at a constant proportion of income whereas the benefit is a known fraction of income at retirement (or some average over income levels in years close to retirement). The consequences of these differences are most apparent in the apportionment of risk under the two types of system. With a defined contributions system, the level of payment into the pension fund is certain for the worker. What is not certain is the maturity value of the pension fund, since this depends on the...

## Personal Retirement Accounts And Social Security Reform

Property Rights and PRAs Most plans currently under consideration would give people the property rights to the funds in their accounts and allow them to be passed along to their heirs in case of death prior to their retirement. However, funds drawn from a PRA during one's retirement years would generally have to be converted to a lifetime annuity, an insurance instrument paying the retiree a regular income for the remainder of his or her life.

## Present Value Of An Uneven Series Of Receipts

The definition of an annuity includes the words fixed amount in other words, annuities involve situations in which cash flows are identical in every period. Although many managerial decisions involve constant cash flows, some important decisions are concerned with uneven cash flows. Consequently, it is necessary to deal with varying payment streams. The PV of the receipts shown in Table A.6 and Figure A.5 can also be found by using the annuity equation the steps in this alternative solution process are as follows Step 2 Recognize that a 200 annuity will be received during years 2 through 5. Thus, we can determine the value of a 5-year annuity, subtract from it the value of a 1-year annuity, and have remaining the value of a 4-year annuity whose first payment is due in 2 years. This result is achieved by subtracting the PVIFA for a 1-year, 6 annuity from the PVIFA for a 5-year annuity and then multiplying the difference by 200 PV of the Annuity (PVIFA6 , 5 - PVIFA6 , a ( 200) (4.2124 -...

## The Institutional Performance Derby The Client Is the Loser

The business of money management can be highly lucrative. It requires very little capital investment, while offering high compensation and the rapid development of what is effectively an annuity. Once an investment management business becomes highly profitable, it is likely to remain that way so long as clients do not depart in large numbers. In the money management business management fees paid by new clients constitute almost pure profit. Similarly, lost fees resulting from client departures affect profitability nearly dollar for dollar, since there are few variable costs to be cut in order to offset lost revenues.

## LP Pension Funding Model

Many companies also provide their employees with so-called defined benefit pension plans. Under defined benefit plans, employers usually offer workers a fixed percentage of their final salary as a retirement annuity. In a typical arrangement, a company might offer employees a retirement annuity of 1.5 of their final salary for each year employed. A 10-year veteran would earn a retirement annuity of 15 of final salary, a 20-year veteran would earn a retirement annuity of 30 of final salary, and so on. Because each employee's retirement benefits are defined by the company, the company itself is obligated to pay for promised benefits. Over time, numerous firms have found it increasingly difficult to forecast the future rate of return on invested assets, the future rate of inflation, and the morbidity (death rate) of young, healthy, active retirees. As a result, several organizations have discontinued traditional defined benefit pension plans and instead have begun to offer new defined...

## When Capital or Operating Costs Are Non Monotonic

As the number of years increases, this approach for calculating the EAC becomes more difficult, especially since in this case the operating costs are neither a standard annuity nor an arithmetic gradient. An alternative is to calculate the present worths of the operating costs for each year. The EAC of the operating costs can be found by applying the capital recovery factor to the sum of the present worths for the particular service period considered. This approach is particularly handy when using spreadsheets.

## Benelux F0

He was against artificial attempts to increase trade, e.g. by having colonies, because he believed that trade is limited by capital. His Manual of Political Economy (1793-5) dealt with international trade. He took to public finance in Supply without Burthen (1795) in which he combined a minimal view of the state with a new proposal to raise the small amount of taxation still necessary - the public auction of all properties in vacant possession because no relatives were alive to inherit. Further, in A Plan for Augmentation of the Revenue (1794-5), he proposed a reduction in the national debt by the use of government-run lotteries and government dealings in life annuities. His Proposal for the Circulation of a New Species of Paper Currency (1795-6) argued that a govern ment monopoly on the issue of paper currency is a cheaper form of government borrowing than the issue of interest-bearing bills. Circulating Annuities (1800) also suggested a new type of paper currency, and in True Alarm...

## Marx Rich or Poor

Sympathetic historians have always noted the poor conditions under which Marx lived, but during most of his life it was not for lack of money. Historian Gary North investigated Marx's income and spending habits, and concluded that except for his self-imposed poverty of 1848-63, Marx begged, borrowed, inherited, and spent lavishly. In 1868, Engels offered to pay off all the Marxes' debts and provide Marx with an annuity of 350 a year, a remarkable sum at the time. North concludes He was poor during only fifteen years of his sixty-five-year career, in large part due to his unwillingness to use his doctorate and go out to get a job. . . . The philosopher-economist of class revolution the 'Red Doctor of Soho' who spent only six years in that run-down neighborhood was one of England's wealthier citizens during the last two decades of his life. But he could not make

## Review Problems

First, the 100 000 paid at the end of 10 years can be thought of as a future amount which has an equivalent annuity. For the first tunnel, the equivalent annuity for the maintenance and pumping costs is First, the Si00 000 paid at the end of 10 years can be thought of as a future amount that has an equivalent annuity of Since the tunnel will have (approximately) an infinite life, an annuity equivalent to the initial cost can be found using the capitalized cost formula, giving a total annual cost of For the first tunnel, the equivalent annuity for the maintenance and pumping costs is Now, for the second tunnel, basically7 the same calculation is used, except that the annuity must be discounted by 20 years at 8 , since the second tunnel will be built 20 years in the future.

## Present Value

Although many goods and services are bought for immediate use, many other benefits come in a stream over time, whether as a season's ticket to baseball games or an annuity that will make monthly pension payments to you after you retire. That whole stream of benefits may be purchased at a given moment for what economists call its present value. However, more is involved than simply determining the price to be paid, important as that is. The implications of present value affect economic decisions and their consequences, even in areas that are not normally thought of as economic, such as determining the amount of natural resources available for future generations.

## Evidence

Another way to circumvent the difficulty to distinguish empirically between adverse selection and moral hazard is to consider the annuity market. Annuity market provides insurance against the risk of outliving accumulated resources. It is more valuable to those who expect to live longer. In this market we can safely expect that individuals will not substantially modify their behavior in response to annuity income (like exerting more effort to extend length of life). It follows that differential mortality rates for annuitants who purchase different types of annuities is convincing evidence that selection occurs. Finkesltein and Poterba (2004) obtain evidence of the following selections patterns. First, those who buy back-loaded annuities are longer-lived (controlling for all observables) than other annuitants which is consistent with the fact that an annuitant with a longer life expectancy is more likely to be alive in later years when the back-loaded annuity pays out more than the...

## Insurance

Insurance companies often sell annuities as well as insurance, using similar principles to payoff the living in installments, instead of paying survivors in a lump sum. Here too, government programs may be analogized to the activities of insurance companies, without in fact having either the same incentives or the same results. The most fundamental difference between private annuities and government pensions is that the former create real wealth by investing premiums, in order to be able to pay pensions later on, while the latter simply use current premiums from the working population to pay current pensions to the retired population. What this means is that a private annuity invests the premiums that come in-creating homes, factories, or other tangible assets whose earnings will later enable the annuities to be paid to those whose money was used to create these assets. Government pension plans, such as Social Security in the United States, simply spend the premiums as they are...

## Discounting

Was used to calculate the present value, P, when a single future value, S, is discounted at r interest continuously for t years. We also discussed the idea of an annuity. This is a fund that provides a series of discrete regular payments and we showed how to calculate the original lump sum needed to secure these payments for a prescribed number of years. This amount is called the present value of the annuity. If the fund is to provide a continuous revenue stream for n years at an annual rate of S dollars per year then the present value can be found by evaluating the definite integral

## The Royal Society

As the bases for further calculations about the amounts of money necessary to pay off life annuities and life insurance policies. (So persuasive was his presentation that some traders began to sell policies. Alas, Halley lacked knowledge of sampling, and speculators were economically ruined )

## Richard E Wagner

A pure regime of collective inheritance is almost certainly impossible in modern societies. There are several related reasons why any effort to tax estates at 100 per cent would collect little, if any, revenue. The effort to impose such a tax would induce people who had accumulated wealth during their lifetime to consume it before their death, by doing such things as converting that wealth into annuities. It would also induce such people to transfer more of their wealth while they were alive, though this possibility would also lead the state to attempt to tax gifts, which in turn would further induce prospective donors to seek methods of doing this none the less. Furthermore, deaths typically are known to heirs before they are known to tax officials, and collective inheritance would surely induce heirs to scavenge among the decedent's assets, particularly among those assets for which titles are not recorded publicly, before officers of the state even arrive on the scene to press their...

## Figure A5

Either of the two methods can be used to solve problems of this type. However, the alternative (annuity) solution is easier if the annuity component runs for many years. For example, the alternative solution would be clearly superior for finding the PV of a stream consisting of 100 in year 1, 200 in Years 2 through 29, and 1,000 in year 30.

## Side Note

Most mortgages are fixed rate mortgage loans, and they are basically annuities. They promise a specified stream of equal cash payments each month to a lender. A 30-year mortgage with monthly payments is really a 360-payments annuity. (The annu-ity formula should really be called a month-ity formula in this case.) What would be your monthly payment if you took out a 30-year mortgage loan for S500,000 at a quoted interest rate of 7.5 per annum A 30-year mortgage is an annuity with 360 equal payments with a discount rate of 0.625 per month. Its PV of S 500,000 is the amount that you are borrowing. You want to determine the fixed monthly cash flow that gives the annuity this value