The present value of an annuity is the current, lump sum value of periodic future payments as calculated using a specific rate. The present value is based on the concept of the time value of money, which states that a dollar today is worth more than a dollar in the future -- $10,000 received today is worth more than receiving $2,000 for the next five years, even though the nominal amount received is the same. This is because once a person has the money she can invest it to earn more money.
To determine the present value of an annuity, one must discount the cash flow by the prevailing discount rate. The higher the rate, the lower the present value. This is logical because the discount rate equals the interest rate an investor would have been paid had she received the money in a lump sum and invested it. In essence it’s the income she “missed” because she didn’t have the funds currently.
The formula to calculate the present value of an annuity is:
PV of annuity = C x [(1-(1+i)^-n)/i]
Where C equals the periodic cash flow, i equals the interest rate and n equals the number of payments.
Taking the example earlier of $2,000 for five years and assuming the interest rate is 5%, the present value of that annuity is calculated as:
$2,000 x [(1-(1+.05)^-5)/.05] =$8,958.95
Which is less than $10,000.
In This Series
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