PV of a Growing Annuity Calculator

Growing Annuity Formula:

\[ PV = \frac{PMT}{r - g} \times \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right] \]

Initial Periodic Payment (PMT):

USD

Discount Rate (r):

decimal

Growth Rate (g):

decimal

Number of Periods (n):

unitless

Present Value (PV):

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1. What is a Growing Annuity?

A growing annuity is a series of periodic payments that increase at a constant growth rate each period. This calculator determines the present value of such cash flows, accounting for both the time value of money and the growth in payments.

2. How Does the Calculator Work?

The calculator uses the growing annuity formula:

\[ PV = \frac{PMT}{r - g} \times \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right] \]

Where:

\( PV \) — Present value of the growing annuity
\( PMT \) — Initial periodic payment amount
\( r \) — Discount rate per period
\( g \) — Growth rate of payments per period
\( n \) — Number of periods

Note: The formula assumes \( r \neq g \). When \( r = g \), the formula simplifies to \( PV = PMT \times n / (1 + r) \).

3. Importance of PV Calculation

Details: Calculating the present value of growing cash flows is essential for investment analysis, retirement planning, and valuing financial instruments with increasing payments.

4. Using the Calculator

Tips: Enter all values as positive numbers. The discount rate and growth rate should be entered as decimals (e.g., 5% = 0.05). Ensure the discount rate is greater than the growth rate for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a growing annuity and regular annuity?
A: A regular annuity has constant payments, while a growing annuity's payments increase by a fixed rate each period.

Q2: Can the growth rate exceed the discount rate?
A: Mathematically yes, but in practice this leads to infinite present value as n approaches infinity, which isn't realistic.

Q3: What are common applications of this formula?
A: Valuing stocks with growing dividends, pension obligations with COLA adjustments, and leases with escalator clauses.

Q4: How does compounding frequency affect the calculation?
A: All rates must match the period length. For annual payments use annual rates, for monthly use monthly rates, etc.

Q5: What happens when growth rate equals discount rate?
A: The formula becomes undefined (division by zero), requiring a different simplified formula.