Ordinary Annuity (payments at end of period)
Annuity Due (payments at beginning of period)
Understanding Present Value of Annuity
The Present Value (PV) of an Annuity is a fundamental concept in finance that helps determine the current worth of a series of future equal payments, discounted at a specific rate. In simpler terms, it answers the question: "How much is a stream of future payments worth today?" This is crucial for making informed investment, retirement planning, and financial decision-making.
What is an Annuity?
An annuity is a financial product or a series of equal payments made at regular intervals for a specified period. These payments can be received (like retirement income) or paid out (like loan installments).
Types of Annuities Relevant to PV Calculation:
Ordinary Annuity: Payments are made at the end of each period (e.g., monthly rent paid at the end of the month).
Annuity Due: Payments are made at the beginning of each period (e.g., a lease payment made at the start of the month).
The Math Behind the Present Value of Annuity
The calculation depends on whether the annuity is ordinary or an annuity due. The core idea is to discount each future payment back to its present value using a discount rate (often representing an interest rate or required rate of return).
Formula for Ordinary Annuity:
The present value (PV) of an ordinary annuity is calculated as:
PV = PMT * [ 1 - (1 + r)^(-n) ] / r
Where:
PV = Present Value of the Annuity
PMT = Periodic Payment Amount
r = Interest Rate per Period (as a decimal)
n = Number of Periods
Formula for Annuity Due:
The present value (PV) of an annuity due is calculated as:
PV = PMT * [ 1 - (1 + r)^(-n) ] / r * (1 + r)
Notice that the annuity due formula is simply the ordinary annuity formula multiplied by (1 + r), because each payment is received one period earlier.
Why Use a PV of Annuity Calculator?
Investment Decisions: Comparing investment opportunities with different payment streams.
Retirement Planning: Estimating the lump sum needed today to fund a desired retirement income stream.
Lease vs. Buy Analysis: Determining the current value of lease payments versus purchasing an asset.
Valuation: Assessing the worth of businesses or assets that generate regular cash flows.
Example Calculation:
Let's say you are to receive $1,000 at the end of each year for 5 years, and your required rate of return (discount rate) is 8% per year. This is an ordinary annuity.