Present Value of an Annuity Due
A level stream of beginning-of-period payments valued today. Each payment arrives one period earlier than in an ordinary annuity, so the value is higher by one period of interest.
PV of Annuity Due (Annual Compounding)
Present value of payments made at the beginning of each year.
When to use: Use to value leases, insurance, or other beginning-of-period payments.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity Due | Total present value of beginning-of-period payments | $ |
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Office Lease
An office lease requires $24,000/year paid at the start of each year for 10 years. Discount rate is 7%.
Given
Step-by-Step
For these inputs, Present Value of Annuity Due is $180,365.57 under the stated payment, compounding and accounting assumptions.
Example 2: Insurance Annuity
An insurance annuity pays $15,000/year at the start of each year for 20 years at 5% discount.
Given
Step-by-Step
For these inputs, Present Value of Annuity Due is $196,279.81 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
Use this annuity due formula. Enter the annual lease payment as PMT, the discount rate as k, and the lease term as n. The result is the total present cost of the lease, accounting for the timing of payments at the start of each period.
Because payments arrive one period sooner, each payment is discounted one less period, making it worth more in present value terms. The PV of an annuity due equals the ordinary annuity PV multiplied by (1 + k).
Insurance companies use this formula to calculate the present value of premium streams paid at the start of each period. It helps determine how much reserve to set aside today to cover future obligations funded by those premiums.
The calculator uses the finite zero-rate limit: an annuity’s value is payment times payment count; a solved payment is the target value divided by a positive payment count. Deferral has no effect at zero interest. Values require whole payment counts, even under continuous interest compounding.