Variables
Description
What is this formula?
The Present Value of an Annuity Due calculates the current value of a series of equal payments made at the beginning of each period.
Because payments are received or paid one period earlier than in an ordinary annuity, the present value is greater than the equivalent ordinary annuity.
When to use it
Use this formula when payments occur at the beginning of each period and you need to determine their equivalent value today.
Example
Suppose:
PMT = $1,000
i = 0.01 per month
n = 12 months
Formula:
PV=PMT((1-(1+i)^(-n))/i)(1+i)
Substitution:
PV=1000((1-(1.01)^(-12))/0.01)(1.01)
PV=11,367.63
Result:
Present Value = $11,367.63
Applications
Lease analysis
Insurance contracts
Retirement planning
Loan evaluation
Investment analysis
Financial planning
Note
This formula assumes equal payments made at the beginning of each period and a constant interest rate. Real financial arrangements may involve changing interest rates, fees, inflation, taxes, or irregular payment schedules that affect the actual present value.