PART OFAnnuity Definition and Guide
Present Value of an Annuity
By
JULIA KAGAN
Reviewed by
ERIC ESTEVEZ Updated Jul 24, 2021
What Is Present Value of an Annuity?
The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate. The higher the discount rate, the lower the present value of the annuity.
KEY TAKEAWAYS
• The present value of an annuity refers to how much money would be needed today to fund a series of future annuity payments.
• Because of the time value of money, a sum of money received today is worth more than the same sum at a future date.
• You can use a present value calculation to determine whether you'll receive more money by taking a lump sum now or an annuity spread out over a number of years.
Understanding Present Value of an Annuity
Because of the time value of money, money received today is worth more than the same amount of money in the future because it can be invested in the meantime. By the same logic, \$5,000 received today is worth more than the same amount spread over five annual installments of \$1,000 each.
The future value of money is calculated using a discount rate. The discount rate refers to an interest rate or an assumed rate of return on other investments over the same duration as the payments. The smallest discount rate used in these calculations is the risk-free rate of return. U.S. Treasury bonds are generally considered to be the closest thing to a risk-free investment, so their return is often used for this purpose.
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Present Value of an Annuity
Example of Present Value of an Annuity
The formula for the present value of an ordinary annuity, as opposed to an annuity due, is below. (An ordinary annuity pays interest at the end of a particular period, rather than at the beginning, as is the case with an annuity due.)
P=PMT×
r
 1−( (1+r)n1 )

where:
P=Present value of an annuity stream
PMT=Dollar amount of each annuity payment
r=Interest rate (also known as discount rate)
n=Number of periods in which payments will be made
Assume a person has the opportunity to receive an ordinary annuity that pays \$50,000 per year for the next 25 years, with a 6% discount rate, or take a \$650,000 lump-sum payment. Which is the better option? Using the above formula, the present value of the annuity is:
Present value
=\$50,000×
0.06
 1−( (1+0.06)251 )

=\$639,168
Given this information, the annuity is worth \$10,832 less on a time-adjusted basis, so the person would come out ahead by choosing the lump-sum payment over the annuity.
An ordinary annuity makes payments at the end of each time period, while an annuity due makes them at the beginning. All else being equal, the annuity due will be worth more in the present.
With an annuity due, in which payments are made at the beginning of each period, the formula is slightly different. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):
P=PMT×
r
 1−( (1+r)n1 )
×(1+r)
So, if the example above referred to an annuity due, rather than an ordinary annuity, its value would be as follows:
Present value
=\$50,000×
0.06
 1−( (1+0.06)251 )
×(1+.06)
=\$677,518
In this case, the person should choose the annuity due option because it is worth \$27,518 more than the \$650,000 lump sum.
Why is Future Value (FV) Important to investors?
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. It is important to investors as they can use it to estimate how much an investment made today will be worth in the future. This would aid them in making sound investment decisions based on their anticipated needs. However, external economic factors, such as inflation, can adversely affect the future value of the asset by eroding its value.
How Does Ordinary Annuity Differ From Annuity Due?
An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. An example of an ordinary annuity includes loans, such as mortgages. The payment for an annuity due is made at the beginning of each period. A common example of an annuity due payment is rent. This variance in when the payments are made results in different present and future value calculations.
What Is the Formula for the Present Value of an Ordinary Annuity?
The formula for the present value of an ordinary annuity is:
P=PMT×
r
 1−( (1+r)n1 )

where:
P=Present value of an annuity stream
PMT=Dollar amount of each annuity payment
r=Interest rate (also known as discount rate)
n=Number of periods in which payments will be made
What Is the Formula for the Present Value of an Annuity Due?
With an annuity due, in which payments are made at the beginning of each period, the formula is slightly different than that of an ordinary annuity. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):
P=PMT×
r
 1−( (1+r)n1 )
×(1+r)
Related Terms
Future Value of an Annuity
The future value of an annuity is the total value of a series of recurring payments at a specified date in the future. more
Annuity Table Definition
An annuity table is a tool for determining the present value of an annuity or other structured series of payments. more
Ordinary Annuity
An ordinary annuity is a series of equal payments made at the end of each period over a fixed amount of time. more
Digging into Annuity Due
Annuity due is an annuity with payment due at the beginning of a period instead of at the end. See how to calculate the value of an annuity due. more
Bond Floor Definition
Bond floor refers to the minimum value a specific bond should trade for and is derived from the discounted value of its coupons plus redemption value. more
How to Calculate Present Value, and Why Investors Need to Know It
Present value is the concept that states an amount of money today is worth more than that same amount in the future. In other words, money received in the future is not worth as much as an equal amount received today. more
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