Present Value of a Growing Annuity Due
A growing annuity whose payments arrive at the beginning of each period, valued today.
PV of Growing Annuity Due
Present value of a growing annuity with payments at the beginning of each period.
When to use: Use when growing payments are made at the start of each period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity | Present value of growing payments | $ |
| PMT | First Payment | The first payment amount | $ |
| k | Interest Rate | Discount rate | % |
| g | Growth Rate | Payment growth rate | % |
| n | Number of Years | Number of periods | years |
Real-Life Examples
Example 1: Prepaid Growing Lease
A lease starts at $5,000/year, growing 2%/year for 10 years, payments at start. Discount rate 6%.
Given
Step-by-Step
For these inputs, Present Value of Annuity is $42,309.88 under the stated payment, compounding and accounting assumptions.
Example 2: Growing Contributions
First contribution $3,000, growing 5%/year for 15 years, at start of year. Discount rate 9%.
Given
Step-by-Step
For these inputs, Present Value of Annuity is $35,091.61 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
Growing annuity due payments occur when escalating payments are made at the start of each period. Examples include leases with annual rent increases paid at the beginning of each year, or subscription services with periodic price hikes billed in advance.
The annuity due version multiplies the ordinary growing annuity present value by (1 + k). This accounts for each growing payment arriving one period earlier, making the entire stream worth more in present value terms.
Yes. Set PMT to the first year's lease payment, g to the annual escalation rate, k to the discount rate, and n to the lease term. The result is the total present value of all escalating beginning-of-period payments.