Present Value of Annuity Calculator
Find today's value of a stream of future payments.
Value a series of equal future payments in today's money.
How the Math Works
The Present Value of Annuity formula calculates the current worth of a series of future payments by discounting each payment back to today's value. The formula PV = PMT × (1 − (1+r)−n) ÷ r works by taking each periodic payment (PMT), factoring in the discount rate (r), and accounting for the number of periods (n). The term (1 − (1+r)−n) represents the present value factor, which captures how much all future payments are worth in today's dollars, while dividing by r adjusts for the time value of money.
Practical Applications
To use this calculation, identify your periodic payment amount, determine an appropriate discount rate based on market conditions or your required rate of return, and count the total number of payment periods. For example, if you're analyzing a 5-year annuity paying $1,000 monthly with a 6% annual discount rate, you'd calculate PMT as $1,000, r as 0.5% (0.06/12), and n as 60 months. This helps compare different annuity options, evaluate lease agreements, or determine how much to invest today to meet future cash flow needs.
Day-to-Day Use
This calculation empowers you to make informed financial decisions in everyday situations like comparing insurance premiums, evaluating whether to lease or buy equipment, or determining if a subscription service offers good value. When planning for major purchases, retirement, or even evaluating job offers with different compensation structures, knowing the present value helps you understand what future payments are truly worth today, preventing you from being swayed by large nominal amounts that may actually be worth less when adjusted for inflation and opportunity cost.
Worked example
$10,000/yr for 15 yr at 5% → ~$103,797.
FAQ
Use?
Pricing pensions, leases and structured settlements.