How would you describe the concept of Future Value of Annuity?
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An annuity is a series of equal payments that occur at evenly spaced intervals. Like rental payments, car payments, etc.\n\nThe future value of an annuity is the value of those payments accumulated and with the compounded interest.\nFor example, if you placed $50 a month in the bank earning 5% interest for 12 months. The amount you would end up with is the future value of an annuity.
472291
You run a bank and a competing bank has a branch across the street.\n\nYou compound your interest annually. So you use the formula: A = P * (1+i)^n.\n\nThe bank across the street says, "We'll compound your interest every month. Their formulate is: A = P * (1+i/12)^(n*12), which gives the customer a little better deal.\n\nOkay, this means war. You start advertising weekly compound interest, or: A = P * (1+i/52)^(n*52), which is a slightly even better deal.\n\nThe other bank compounds daily.\n\nSo you decide to take it as far as you can go. You'll compound continuously. You're formula is:\n\nA = P * (1+i/x)^(n*x) as x approaches infinity. \n\nThe bank across the street can't beat that. Oh, there's no infinity button on your calculator, so how do you calculate savings deposits?\n\nBy running this formula through limit theory, you use the fact that (1+1/x)^x as x approaches infinity is e, and you get the following formula:\n\nA = P*e^(i*n) for continuous compounding.\n\nI don't know of any bank that calculates interest continuously, but there are at least two natural phenomenons that change at a continuous rate.\n\nThe first is population growth, such as the number of humans on the plant, or the number of bacteria in a jar.\n\nThe other is radioactive decay, which is often described as "half-life."\n\nBoth of these natural behaviors are defined by the continuous growth formula, and it cannot be derived without limit theory.\n\nBy the away, we pretty much define calculus using limit theory, but one could argue that calculus isn't part of daily life.
488542
I would describe it as "well-established" or "long-standing." In today's economy I think those descriptions fit a 30-year-old company.
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In other words, you want to know how much is the stream of payments worth today in a lump sum.  This is a really simple calculator that can tell you what that stream of payments is worth as a lump sum.  \nhttp://www.deseretfirstcu.org/calc/pvannuity.asp\nThe two main variables are, what interest rate is the company using and how long is the stream of payments?  If the stream of payments was going to be for lifetime, you would have to know what age their actuarials came up with for their calculation.\n\nI hope this helps.  Good luck.
1164552
Do you mean the present value of annuity of 1 per year, for 48 years, at 8% per year compounded annually?\n\n\n(1-(1/1.08^48))/0.08 = 12.19
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if interest is compounded daily, don't forget to...\n\n1.  divide 5.16% by 365 to get the daily rate\n2.  use 30 days as your period "n"\n3.  don't use the avg daily balance.  you must use the initial principal balance at the beginning of the 30 day period.\n\ni haven't worked it out, but if your formula is correct, the future value will work.\n\nif you have a business calculator (preferrably from HP)\n\nPV = initial principal balance\ni = 5.16% divided by 365 days\nn = 30 days\n\nsolve for FV
262223
Vanguard has very good rates for annuities.  However, if you are making the arrangements, that suggests the geriatric patient may not be in good health, and does not have a long life expectancy.  Annuities are best for people who have a long life expectancy.  You may need to talk to an insurance agent.  Unfortunately, they charge a lot in commissions.\nYou don't make your position clear.  Are you a health care worker and this person is your patient?  Are you a relative, and you're trying to make your parent self-sufficient so you don't have to support them?  The advice is quite different depending on the situation.  Tell us more!
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It depends.  Usually people buy annuity to buy the peace of mind that they won't run out of money if they live too long.\n\nEquity Index annuity is an annuity where the cash value and death benefit both depends on a specific equity.  \n\nLike invest in stock market, you want longer time horizon.  Also read all the fine prints in details.\n\nAlso, ask the agent to quote the premiums of a term life, whole life and universal life policy for you so you know what you're really paying.
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In theory, a stock's price should be equal to the present value of all of its future cash flows.  Anything that causes the cash flows to get bigger or smaller has an effect on price.  But given that cash flows don't change, the price can still change if the interest rate changes.\n\nLet's look at an example.  Suppose that you have a company that has paid all of its bills for the next year.  In one year, it gets a $100,000,000 payment for sure.  At that time, the payment will be distributed to all owners of the firm & the firm will disolve.  How much is the firm worth?  We know it will be worth $100MM in a year.  What is the right interest rate.  Suppose is it 10%.  Can we find the value of the firm now?  Sure -- it is the amount that if we invest it at 10% it will be worth $100MM in a year.  That is, it is worth $100MM/1.1 or $90,909,090.91 now.  \n\nOK -- what happens if interest rates change.  Perhaps they go up to 11%.  Then the value of our firm changes to $100MM/1.11 = $90,090,090.09 -- losing almost $82K in value.  If rates go down, the value should go up.\n\nNext, let's look at CPI.  This is the rate of inflation.  If it increases, people will think that they need more money to have the same lifestyle in the future.  If they are worried about inflation, they will demand a higher interest rate to compensate them for higher prices in the future.  So, changes in expected inflation change the interest rates, and therfore change stock prices.\n\nWhat about the economic growth rate?  If the economy grows faster than expected, then maybe that $100MM that we thought the company was going to get will be higher.  A higher payment translates into higher stock prices.\n\nAs for employment, it turns out that the employment rate is associated with growth.  If a lot of companies are hiring, then there will be more money spent by the new employees, and there will be more produced by those new employees, so demand for goods goes up.  This causes an increase in the expected profits, and higher stock prices.  It isn't quite so simple, though.  If there are too many people working, then the demand for labor causes higher costs and lower profits, which causes stock prices to decline.
836630
Example for a geometric series:\nSuppose you apply for a $10000 loan at a bank and you would like to repay it in 10 years in uniform yearly payments. The interest rate is 10%. How much is your yearly payment going to be ?\n\nIn finance, getting a dollar next year is worth less than getting a dollar now. It is because if the interest rate is 10% then if you have a dollar now and lend it to the bank for a year then you'll have $1.1 next year. How much of today's money is equivalent to $1 next year? The answer is 1/1.1, because if you have $ 1/1.1 dollar now and invest it for a year then you'll have exactly $ 1/1.1 * 1.1 = $1 next year. Similarly, having $1 in two years is equivalent to having $1/1.1^2 now. This is the so-called present value of future payments. Dividing by 1.1, 1.1^2 etc. is called discounting.\n\nThis means that if your yearly uniform payment is denoted by let's say C, then, in present value, the bank will get:\n\n$ C/1.1 + C/1.1^2 + C/1.1^3 + ... + C/1.1^10 from you.\n\nThis can be summed up using the formula for a geometric series:\n\nq + q^2 + q^3 + ... + q^n = (1-q^n)*q/(1-q), and in our case, q=1/1.1, and the sum is:\n\n$ C*q + C*q^2 + C*q^3 + ... + C*q^n = C*(1-q^n)*q/(1-q) = 6.14*C.\n\nAssuming that all charges and profit of the bank is included in the interest rate, the bank will be willing to give you $10000 if the present value of its future incomes from you is $10000:\n\n6.14 * C = $10000, which yields\nC=1627.45.\n\nThis means that your yearly payment will be $1627.45.\n\nFinance uses geometric series all the time. I'll leave the other applications to the rest of the answerers.
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Expenses are generally higher in variable annuities than mutual funds but there are no front-end loads to deal with and annuities can offer things that mutual funds can't - like guarantees. \n\nAnnuities may help you 1)Receive guaranteed retirement income payments for as long as you live, 2)Protect beneficiaries with a death benefit 3)Diversify your investments. 4)Grow assets on a tax-deferred basis and 5)Avoid outliving your assets.\n\nIf you want to protect your beneficiaries, variable annuities generaly offer a choice of death benefits to protect assets for your beneficiaries should you die prior to annuitization. Also, a variable annuity’s death benefit avoids the expense and delays of probate.\n\nIf you're concerned about the volatility of the stock market some variable annuities offer an “Income Benefit” feature. This optional feature (available for an additional fee) can provide you with a minimum level of income (upon annuitizing the contract) should the market decline dramatically. Some variable annuities also offer principal protection features which guarantee that you will get back at least your initial investment after some stated period of time (typically ten years).
1134715
Valuation of financial derivatives (options, futures, forwards, etc)\nReal hard math, but real good money.
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time!  you can earn. and lose money, easy.\n\nyou get one life to live.  Once the time is gone, you never get it back.  Money and credit can be re-earned, but years can never earned back.\n\nAlways value time.  There was once an email that I received that went like this:\n\nTo realize the value of four years, ask a graduate.  \nTo realize the value of 1 year ask a student who has failed a final exam.  \nTo realize the value of 9 months, ask a mother who gave birth to a stillborn.  \nTo realize the value of one month ask a mother who has given birth to a premature baby.  \nTo realize the value of one week, ask an editor of a weekly newspaper.  \nTo realize the value of one hour, ask the lovers who are waiting to meet.  \nTo realize the value of one minute ask a person who has just missed the train, bus or plane.  \nTo realize the value of one second, ask a person who has survived an accident.  Just one second’s difference.  \nTo realize the value of finally one millisecond, ask the person who has won a silver medal in the Olympics.  Just one millisecond.  \n\nTime waits for no one, treasure every moment you have.
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Here is an example of both a present and future value equation:\n\nIt makes it easier the first few times to actually do each payment individually and then add them all up just to conceptualize it, then you can use the formula later as you understand what it is telling you to do:\n\nStart with the easiest Future Value:\n\nFV= PV(1=i)^n\n\nread as future value equals the present value times 1times the interest rate to the nth power where n equals the number of frequencies.  It is of course vital then to have an interest rate to use so that for example if you want to find the future value of 100 at 5% interest in five years the expression looks like this:  FV= 100(1+.05)^5\nThe long version would be: this:\n\nat the end of one year you have 100(1.05)=100p + 5i or 105\nyear 2 you have (dont forget, you have 105 bucks now) 105(1.05)=110.25 and so on......you would then continue to take your future value (110.25 and add the next years interest to it until you did this five times until you arrived at approximately 127.63.\n\nOkay, now for PV:\n\nPV= FV(1+i)^-n\n\nnow you would work this function backwards so that you solve for PV as follows:  PV=212714(1.05)^-5.\n\nYou can apply the same logic as above and get a payment stream and find out what you are left with.\n\nUsing a financial calculater you may use something such as FV=212714, I=5,N=5 then tell it to compute the present value.\n\nUnderstanding the concept is relatively easy once you write it out and look at it.  I hope this helps.  Using a website or calculator is nice but if you don't understand how it arrived at the number its no good to you anyway because what if you input a number wrong?  You wouldnt know because you have no logical background to draw from.
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This question can have a number of answers, depending upon which context it refers to.  \n\nFor example, imagine a life insurance company receives premiums on a regular and predictable basis.  They invest most of this money in the equity market.  Then they have to pay out money on life insurance policies as people die.\n\nHow much will they have to pay out?  Well, it depends upon your assumptions.  If you assume that people will more or less live as long as they usually have in the past, then you can use tables of numbers that let you estimate how much money will probably need to be paid out over time.  this is an estimate and cannot be certain, and so some assumptions and mathematical models are used.  Hence the word "modelling".\n\nThe money they have to pay out is their "liability".\n\nTheir assets are whatever they bought with the premiums they received, as in stock.  Will the stock market grow enough so that stock can be sold to pay out on the life policies? That depends on  how you model the returns of the stock market.\n\nIn the past, actuaries assumed that stocks will make as much money as they usually have in the last 20 years or so.  Unfortunately they may be wrong.  Another model that is safer to use is that of "risk neutral valuation" which is a model used in option pricing.  it is also the model used by banks to value their assets and liabilities.\n\nhope that example explains the idea.
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you gotta get some numbers on what happened in the past and will happen in the future. \n\ne.g. Demand forecasts, effect of advertizing, your costs as a function of output, link between employee compensation and perfomance.
418116
When you buy a car, you often take out a loan to pay for the car.  The loan is an annuity; you promise to make payments every month for 3 years.  Whoever gives you the loan does not simply take the price of the car and divide it by 36 to determine how much you will pay.  This is because the lender can put that money in the bank and earn interest.  In order to get a loan, you must pay more than the bank is willing to pay him for his money; the present value of your annuity must be higher than the lent amount plus interest.  Of course, there are other factors like your risk as a borrower, but this is a basic example.  \n\nThe best use of Present Value of Annuity is comparing 2 streams of payments.  As a general rule, you should purchase the financial instrument that has the highest present value.