Present Value of an Annuity Calculator
Present Value of an Annuity Calculator
This calculator helps you estimate the present value (PV) of an annuity - a series of equal payments made over time. By discounting each future payment back to today using an interest rate, you can compare annuities to lump-sum alternatives and make consistent financial decisions across different schedules and markets.
What is the Present Value of an Annuity?
The present value of an annuity is the amount of money today that is equivalent to receiving fixed payments in the future, assuming a discount rate. It is widely used in loans, retirement planning, leases, and investment valuation.
Core Formulas Used
First, compute the periodic rate from the annual rate:
\( r=\frac{i}{m} \)
Where \( i \) is the annual interest rate (decimal form) and \( m \) is the number of payments per year.
For an ordinary annuity (payments at the end of each period):
\[ PV = PMT \cdot \frac{1-(1+r)^{-n}}{r} \]
For an annuity due (payments at the beginning of each period):
\[ PV_{\text{due}} = \left(PMT \cdot \frac{1-(1+r)^{-n}}{r}\right)\cdot(1+r) \]
If the periodic rate is zero (\( r=0 \)), the formula reduces to:
\[ PV = PMT \cdot n \]
How to Use This Calculator
Step 1 - Enter the payment amount
Provide the fixed amount paid each period (\(PMT\)).
Step 2 - Set the annual interest rate
Enter the annual percentage rate used for discounting. The calculator converts it into a periodic rate based on your payment frequency.
Step 3 - Choose payments per year and total payments
Payments per year defines the compounding/payment frequency, and total number of payments defines the length of the annuity.
Step 4 - Select payment timing
Choose End of Period for an ordinary annuity, or Beginning of Period for an annuity due.
Interpreting the Results
The calculator returns:
- Present Value (PV) - the discounted value today of all future payments
- Periodic Rate - the per-period discount rate derived from the annual rate
- Discount Factor - the multiplier applied to \(PMT\) to compute PV
- Total Payments - the sum of all payments without discounting
Practical Use Cases
Loan and lease comparisons
Use PV to compare different payment schedules on an apples-to-apples basis.
Retirement and pension valuation
Estimate how much a stream of future payments is worth today given a discount rate.
Investment decision support
Evaluate whether taking an annuity stream is preferable to a lump-sum amount.