Growing Annuity Calculator
Print
The Growing Annuity Calculator helps financial analysts, investors, and pre-retirees compute the Present Value (PV) and Future Value (FV) of a series of recurring cash flows that increase at a constant annual growth rate (g). Evaluate inflation-protected pension streams, expanding royalty payments, and escalating corporate lease cash flows.
The Growing Annuity Formulas
Present Value (PV) and Future Value (FV) of a growing ordinary annuity (where discount rate r is greater than growth rate g) are calculated as follows:
Present Value (PV) = [ C / ( r - g ) ] × [ 1 - ( ( 1 + g ) / ( 1 + r ) )^n ]
Future Value (FV) = [ C / ( r - g ) ] × [ ( 1 + r )^n - ( 1 + g )^n ]
Where:
- C: Initial first-period cash flow payment amount.
- g: Constant annual payment growth rate (e.g., 3.00% annual inflation adjustment).
- r: Annual discount rate or target rate of return.
- n: Total number of payment periods (years).
Growing Annuity Valuation Benchmarks
Compare Present Value (PV) and Future Value (FV) for an initial $10,000 annual payment growing at 3.00% per year across discount rates (10-year horizon):
| Annual Discount Rate (r) | Annual Cash Growth Rate (g) | Present Value (PV) | Future Value (FV @ Yr 10) | Total Nominal Cash Paid |
|---|---|---|---|---|
| 6.00% APR | 3.00% / year | $84,043.10 | $150,508.60 | $114,638.80 |
| 8.00% APR | 3.00% / year | $75,702.40 | $163,436.50 | $114,638.80 |
| 10.00% APR | 3.00% / year | $68,495.20 | $177,665.40 | $114,638.80 |
Step-by-Step Growing Annuity Calculation Example
Here is an example calculating the Present Value of a 5-year lease stream starting at $20,000/year, growing at 4.00% annually, discounted at 7.00% APR:
- Identify Inputs: C = $20,000, g = 4.00% (0.04), r = 7.00% (0.07), n = 5 years.
- Calculate Rate Difference (r – g):
0.07 - 0.04 = 0.03. - Calculate Growth-Discount Factor:
( (1 + 0.04) / (1 + 0.07) )^5 = ( 1.04 / 1.07 )^5 = 0.8665. - Apply Present Value Formula:
[ $20,000 / 0.03 ] × [ 1 - 0.8665 ] = $666,666.67 × 0.1335 = $88,995.50. - Result: The present value of the 5-year growing lease stream is $88,995.50.
Frequently Asked Questions
What is a growing annuity?
A growing annuity is a financial product or cash stream where recurring payments increase by a fixed percentage (g) every compounding period for a specified duration (n).
What happens if the growth rate (g) equals the discount rate (r)?
If the growth rate equals the discount rate (g = r), the standard formula produces a division by zero error. In this special case, the present value simplified formula is: PV = n × C / ( 1 + r ).
Why are growing annuities important for retirement planning?
Growing annuities model real-world retirement income needs by factoring in annual inflation rate adjustments, ensuring purchasing power remains constant over decades.
How does a growing annuity differ from a growing perpetuity?
A growing annuity has a fixed end date (finite periods n). A growing perpetuity continues escalating payments indefinitely into eternity.