Present Value of Annuity Calculator
Calculate the present value of a series of equal future cash flows over a given time period
Annuity Parameters
Amount paid in or out for each period
Annual nominal interest rate
How often interest is compounded
How often payments are made
Annual percentage increase in payments (for growing annuity)
Present Value Results
Analysis
Example Calculation
Ordinary Annuity Example
Payment: $7,000 annually for 4 years
Interest rate: 5% annual
Type: Ordinary annuity (payments at year end)
Calculation
PVA = PMT × ((1 / i) - (1 / (i × (1 + i)^n)))
PVA = $7,000 × ((1/0.05) - (1/(0.05 × (1.05)^4)))
PVA = $7,000 × (20 - 16.454)
PVA = $24,822
Annuity Types
Ordinary Annuity
Payments at end of each period
Mortgages, car loans, student loans
Annuity Due
Payments at beginning of each period
Rent, insurance premiums, lottery payoffs
Growing Annuity
Payments increase over time
Inflation-adjusted payments
Key Formulas
Ordinary Annuity
PVA = PMT × ((1/i) - (1/(i×(1+i)^n)))
Annuity Due
PVA = Ordinary PVA × (1 + i)
Growing Annuity
PVA = PMT/(i-g) × (1-((1+g)/(1+i))^n)
Annuity Tips
Annuity due has higher present value than ordinary annuity
Higher interest rates reduce present value
Longer time periods reduce present value
Growing annuities account for inflation
Match payment and compounding frequencies
Understanding Present Value of Annuity
What is Present Value of Annuity?
The present value of an annuity is the current cash value of a series of equal future payments. It shows what those future payments are worth in today's dollars, considering the time value of money.
Key Concepts
- •Time Value of Money: Money today is worth more than the same amount in the future
- •Discount Rate: The interest rate used to calculate present value
- •Payment Timing: When payments occur affects present value
Common Applications
- •Evaluating investment opportunities
- •Pension and retirement planning
- •Loan and mortgage analysis
- •Insurance settlement evaluation
- •Business valuation and cash flow analysis
Important Factors
- •Higher interest rates decrease present value
- •Longer time periods decrease present value
- •Payment frequency affects calculations