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In this lesson, you'll learn about payments that occur at regular time intervals, or in financial terms, annuities. Afterwards, test your understanding of the lesson with a quiz.
What Is an Annuity?
If you're ever lucky enough to win any substantial amount in the lottery, you'll have two choices: take a lump sum now or take payments over a certain number years. An annuity is simply a series of future cash payments that occur at a regular interval. The payments can be different amounts, but must occur regularly - usually monthly, quarterly, or annually.
Examples of Annuity
There aren't a lot of people who experience annuities through lottery winnings that pay out millions of dollars per year, but many people are familiar with another type of annuity - a mortgage payment. A mortgage payment is a regularly occurring series of payments, or annuity, on a real estate loan. These people aren't on the receiving end of the annuity - the bank is.
Some other examples of annuities include life insurance payments, pension payments, regular savings account deposits, and some investments. Financial institutions will sometimes sell annuities, so in exchange for either a one-time payment or a series of payments, the bank will give you your money back, plus interest, at some future time.
The Value of Annuities
If you have an annuity that pays you $1,000 per year for ten years, what is the value - right now - of your annuity? The answer isn't $10,000 as many people might calculate. Instead, calculating the value of an annuity involves a financial concept called the time value of money. Essentially, the idea of the time value of money is simply that money loses its value over time. For example, fifty years ago, you could buy a candy bar for a nickel; now it costs over a dollar. This is due to inflation, during which prices rise and money loses its value. The faster prices rise, the less your future money is worth.
Because money loses its value over time, the actual value of an annuity depends on the interest rate. Interest rates are what determines if $1,000 in ten years can buy the latest tablet computer or a candy bar. When valuing an annuity, you need to select an interest rate. If you are simply trying to save your money and don't want to lose purchasing power, then all you need to do is use the expected inflation rate as your interest rate. If you want to make a 10% return on your money, you need to discount the annuity at 10%.
The formula for calculating the present value of an annuity - the value today of a stream of future payments - is the same whether the payments are the same amount each period or if they vary.
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The formula for calculating the present value of an annuity
In the formula for the present value of an annuity, t is the time period, n is the payment for that period, and i is interest rate. However, if the payment amounts are all equal, the formula can be simplified by combining the terms that calculate each payment amount's value, giving us this formula:
Let's use the formula for an annuity with equal payments to figure out how much we should pay to get $1,000 per year for the next ten years. For our interest rate, let's say we have pretty high standards and want to assume a growth rate of 10%. Remember, in financial formulas, percentages are shown as their decimal values. So, for a 10% return on our money, we pay $6,145 today in exchange for a ten-year, $1,000 payment annuity.
An annuity is simply a series of future cash payments that occur at a regular interval. The payments can be different amounts, but must occur regularly - usually monthly, quarterly, or annually.
Everyday examples of annuities include:
Life insurance payments
Regular savings account deposits
The value of an annuity can be determined with the help of a concept called the time value of money which states that money loses its value over time. This occurs because of inflation, during which prices rise and money loses its value. With this knowledge and the formula for the value of an annuity, you can figure out the real present value of an annuity - the value today of a stream of future payments. Who knows, if you win the lottery, you can use it to decide if you want the lump sum or regular payments!
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