Growing Annuity Calculator
Use this calculator to determine the present value (PV) and future value (FV) of a growing annuity. A growing annuity is a series of payments that grow at a constant rate over a specified number of periods.
Results:
Present Value of Growing Annuity:
Future Value of Growing Annuity:
Understanding the Growing Annuity
A growing annuity represents a stream of payments that increase at a constant rate over a finite number of periods. This financial concept is crucial for various applications, including retirement planning, investment analysis, and valuing certain types of financial instruments.
Key Components:
- First Payment Amount (P): This is the initial payment made at the end of the first period. All subsequent payments will grow from this base.
- Periodic Interest Rate (r): Also known as the discount rate, this is the rate at which future payments are discounted back to their present value, or the rate at which the annuity grows if considering future value. It's expressed as a percentage per period.
- Periodic Growth Rate (g): This is the constant rate at which each payment in the annuity increases from the previous one. It's also expressed as a percentage per period.
- Number of Periods (n): This is the total count of payments or periods over which the annuity is received or paid.
How the Calculator Works:
This calculator determines two key values for a growing annuity:
- Present Value (PV) of a Growing Annuity: This is the current worth of all future growing payments, discounted back to the present using the periodic interest rate. The formula used is:
PV = P * [ (1 - ((1 + g) / (1 + r))^n) / (r - g) ]If
r = g, the formula simplifies to:PV = P * n / (1 + r) - Future Value (FV) of a Growing Annuity: This is the total value of all growing payments at the end of the last period, compounded forward at the periodic interest rate. The formula used is:
FV = P * [ ((1 + r)^n - (1 + g)^n) / (r - g) ]If
r = g, the formula simplifies to:FV = P * n * (1 + r)^(n-1)
Where:
P= First Payment Amountr= Periodic Interest Rate (as a decimal)g= Periodic Growth Rate (as a decimal)n= Number of Periods
Practical Examples:
Let's consider a few scenarios to illustrate the use of the Growing Annuity Calculator:
Example 1: Retirement Savings
You plan to contribute $2,000 to your retirement fund at the end of the first year, and you expect to increase your contributions by 3% each year. Your fund is expected to earn an average annual return of 7%. You plan to do this for 20 years.
- First Payment (P): $2,000
- Periodic Interest Rate (r): 7%
- Periodic Growth Rate (g): 3%
- Number of Periods (n): 20
Using the calculator, you would find the Future Value of this growing annuity, which represents the total amount accumulated in your retirement fund after 20 years.
Example 2: Valuing a Growing Dividend Stream
An investor is analyzing a stock that is expected to pay a dividend of $1.50 per share at the end of the first year, with dividends growing at 4% annually for the next 15 years. The investor requires a 10% rate of return.
- First Payment (P): $1.50
- Periodic Interest Rate (r): 10%
- Periodic Growth Rate (g): 4%
- Number of Periods (n): 15
The Present Value of this growing annuity would help the investor determine the fair value of the future dividend stream today.
Example 3: Project Cash Flows
A company is evaluating a project that is expected to generate a net cash flow of $50,000 in the first year, with cash flows increasing by 2% annually for 5 years. The company's cost of capital is 8%.
- First Payment (P): $50,000
- Periodic Interest Rate (r): 8%
- Periodic Growth Rate (g): 2%
- Number of Periods (n): 5
The Present Value of this growing annuity would provide the current worth of the project's future cash flows, which is a key input for investment decisions.