Present Value of an Annuity

What Is Present Value of an Annuity?

The current value of an annuity is the current value of future payments from an annuity, given a predefined rate of return, or discount rate. The higher the discount rate, the lower the present value of the annuity.

Figuring out Present Value of an Annuity

Due to the time value of money, money received today is worth more than a similar amount of money in the future since it tends to be invested meanwhile. By a similar logic, $5,000 received today is worth more than a similar amount spread north of five annual portions of $1,000 each.

The future value of money is calculated utilizing a discount rate. The discount rate alludes to an interest rate or an assumed rate of return on different investments over similar duration as the payments. The littlest discount rate utilized in these calculations is the risk-free rate of return. U.S. Treasury bonds are generally viewed as the nearest thing to a risk-free investment, so their return is frequently utilized for this purpose.

Illustration of Present Value of an Annuity

The formula for the current value of a ordinary annuity, instead of a annuity due, is below. (An ordinary annuity pays interest toward the finish of a specific period, instead of toward the beginning, similarly as with an annuity due.)
$\begin &\text = \text \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) } \ &\textbf \ &\text = \text \ &\text = \text \ &r = \text{Interest rate (also known as discount rate)} \ &n = \text \ \end$
Assume a person has the opportunity to receive an ordinary annuity that pays $50,000 each year for the next 25 years, with a 6% discount rate, or take a $650,000 lump-sum payment. Which is the better option? Utilizing the above formula, the current value of the annuity is:
$\begin \text &= $50,000 \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + 0.06 ) ^ {25} } \Big ) }{ 0.06 } \ &= $639,168 \ \end$
Given this data, the annuity is worth $10,832 less on a period changed basis, so the person would end up as a winner by picking the lump-sum payment over the annuity.

An ordinary annuity makes payments toward the finish of each time span, while an annuity due makes them toward the beginning. All else being equivalent, the annuity due will be worth more in the present.

With an annuity due, in which payments are made toward the beginning of every period, the formula is marginally different. To track down the value of an annuity due, essentially increase the above formula by a factor of (1 + r):
$\begin &\text = \text \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) } \times ( 1 + r ) \ \end$
Thus, on the off chance that the model above alluded to an annuity due, as opposed to an ordinary annuity, its value would be as per the following:
$\begin \text &= $50,000 \times \frac { 1 - \Big ( \frac { 1 }{ ( 1 + 0.06 ) ^ {25} } \Big ) }{ 0.06 } \times ( 1 + .06 ) \ &= $677,518 \ \end$
In this case, the person ought to pick the annuity due option since it is worth $27,518 more than the $650,000 lump sum.

Features

• In view of the time value of money, a sum of money received today is worth more than a similar sum sometime not too far off.
• The current value of an annuity alludes to how much money would be required today to fund a series of future annuity payments.
• You can utilize a current value calculation to decide if you'll receive more money by taking a lump sum now or an annuity spread out over a number of years.

FAQ

What Is the Formula for the Present Value of an Ordinary Annuity?

The formula for the current value of an ordinary annuity is:$\begin & ext = ext imes \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) } \ & extbf \ & ext = ext \ & ext = ext \ &r = ext{Interest rate (otherwise called discount rate)} \ &n = ext \ \end$

How Does Ordinary Annuity Differ From Annuity Due?

An ordinary annuity is a series of equivalent payments made toward the finish of back to back periods over a fixed timeframe. An illustration of an ordinary annuity incorporates loans, like mortgages. The payment for an annuity due is made toward the beginning of every period. A common illustration of an annuity due payment is rent. This variance in when the payments are made outcomes in different present and future value calculations.

For what reason is Future Value (FV) Important to investors?

Future value (FV) is the value of a current asset sometime not too far off in view of an assumed rate of growth. It is important to investors as they can utilize it to estimate how much an investment made today will be worth later on. This would aid them in settling on sound investment choices in light of their anticipated necessities. Nonetheless, outer economic factors, like inflation, can adversely influence the future value of the asset by eroding its value.

What Is the Formula for the Present Value of an Annuity Due?

With an annuity due, in which payments are made toward the beginning of every period, the formula is marginally different than that of an ordinary annuity. To track down the value of an annuity due, essentially duplicate the above formula by a factor of (1 + r):$\begin & ext = ext imes \frac { 1 - \Big ( \frac { 1 }{ ( 1 + r ) ^ n } \Big ) } imes ( 1 + r ) \ \end$